GB2639189A - A method of calculating exposure to air pollutants - Google Patents

Abstract

A method of calculating exposure to air pollutants comprises receiving a path comprising a sequence of path locations, receiving or retrieving concentration maps corresponding to one or more air pollutants, each concentration map comprising modelled concentration values of the corresponding air pollutant at each of a plurality of model locations, and for each given air pollutant, determining a concentration profile of the given air pollutant as a function of distance along the path by: in response to a pair of sequential path locations being separated by more than a target spacing, inserting one or more interpolation locations between that pair of path locations, so every section of the path longer than the target spacing includes at least one path location or interpolation location. Then for each interpolation location and each path location, a corresponding concentration value is interpolated based on modelled concentration values of the two or more model locations closest to that interpolation location or path location. The concentration profiles of the one or more air pollutants are stored or output.

Description

Intellectual Property Office Application No GI324032997 R TM Date:30 August 2024 The following terms are registered trade marks and should be read as such wherever they occur in this document: Bluetooth, WiFi, Google, Bing, Open Intellectual Property Office is an operating name of the Patent Office www.gov.uk /ipo A method of calculating exposure to air pollutants

Field of the invention

The present invention replated to a method of calculating exposure to air pollutants.

Background

Air pollution is the largest environmental risk to health globally, causing millions of premature deaths and affecting the quality of life of billions of people. To address this challenge, air quality monitoring is conducted around the world, providing vital ground-truth data on the concentration and distribution of various pollutants.

However, air quality monitoring stations are often sparse and unable to truly reflect the complex nature of urban areas, where air pollution can vary significantly across space and time.

Air quality models are becoming increasingly sophisticated, taking in monitoring data and using dispersion modelling and other atmospheric information to create detailed models of air pollution in cities. Such models can provide more spatially and temporally resolved estimated of air pollution than is possible from fixed monitoring alone., but they still have limitations in capturing the individual variability and personal factors that affect the actual exposure and health impact of each person.

The extraordinary rise in use of smartphones over the past 15 years has opened new possibilities for personalizing air quality information. Smartphones are with us all day every day, packed with always-on sensors that provide location, trajectory, temperature, ambient light, orientation, and other data. There are calls from government and the air pollution research community for increasingly personalized air quality information that can help individuals make informed decisions about their health and behaviour (e.g., see McCarron et al., 2023 "Public engagement with air quality data: using health behaviour change theory to support exposure-minimising behaviours", Nature, 33, 321-331).

Personal sensors exist that can measure some pollutants directly, but currently, none on the market can measure all four main regulated pollutants (PM2.s, PMio, NO2, and 03). These sensors can also be also affected by changes in temperature and humidity, are often trapped under clothes, in bags, require charging, and other factors.

Moreover, personal sensors alone cannot provide the context and forecasting capability of air pollution that models can offer.

Therefore, there is a need for a novel method and system that can combine location and activity data from smartphones, optionally personal biometric data from wearable devices or user input, and air quality models to provide unobtrusive, always-on, highly personalized air pollution exposure feedback to everyone at nearly zero marginal cost.

Such a method and system would be massively scalable and have significant potential to improve public health and environmental awareness.

References: McCarron et al., 2023 "Public engagement with air quality data: using health behaviour change theory to support exposure-minimising behaviours", Nature, 33, 321-331.

Satoh, T.; Higashi, T.; Sakurai, H.; Omae, K., "Development of a new exposure monitoring system considering pulmonary ventilation (DEM 1)". The Keio Journal of Medicine 1989, 38, (4), 432-42.

Summary

According to a first aspect of the invention, there is provided a method of calculating exposure to air pollutants. The method comprises receiving a path comprising a sequence of path locations, receiving, or retrieving concentration maps corresponding to one or more air pollutants, each concentration map comprising modelled concentration values of the corresponding air pollutant at each of a plurality of model locations. For each given air pollutant, determining a concentration profile of the given air pollutant as a function of distance along the path by: in response to a pair of sequential path locations are separated by more than a target spacing, inserting one or more interpolation locations between that pair of path locations, so every section of the path longer than the target spacing includes at least one path location or interpolation location. For each interpolation location and each path location, interpolating a concentration value corresponding to that interpolation location or path location based on modelled concentration values of the two or more model locations closest to that interpolation location or path location, storing or outputting the concentration profiles of the one or more air pollutants.

The path locations need not be evenly spaced along a total length of the path.

A convex hull of the array of model locations for the one or more concentration maps may wholly contain the path locations. Receiving or retrieving a concentration map may include receiving or retrieving a portion of a larger concentration map which corresponds to an area including the path locations.

The modelled concentrations of each air pollutant may be determined using models based on measurements obtained from a plurality of measurement stations, and/or using emissions estimates. The measurement stations do not all need to measure each, or the same set, of the one of more air pollutants.

Path locations may comprise coordinates for a position on the earth's surface. Path locations may comprise latitude and longitude. Path locations may comprise cartesian, polar coordinates. Path locations may comprise vertical information, for example, altitude. The vertical information of the path locations may comprise horizontal information to estimate position, which can be used to estimate vertical location information, e.g., using topography information.

Model locations may be in a regular grid. Model locations may be spaced apart by 1, 5, 10, 20, or 50 m. Preferably, the model locations are spaced apart by 20 m or less.

The concentration profile of the given air pollutant may be a function of distance and time along the path.

Inserting one or more interpolation locations may comprise calculating those locations.

The path may comprise biometric data.

The concentration value may be interpolated using a time-weighted average between each path location. That is, using the time between two path locations and the mean concentration of a given air pollutant at those two path locations, and the interpolation locations between the path locations to calculate the time-weighted average between the two path locations with respect to the whole journey.

The concentration value may be interpolated using bilinear interpolation of the four closest model locations to each interpolation location or path location.

The path locations and/or the interpolation locations may comprise longitude and latitude.

The path locations may be determined from data comprising satellite data.

The path location may be derived based on location data from a smartphone, for example, from short-range wireless technology (e.g., Bluetooth), or wireless network protocols based on the IEEE 802.11 family of standards (e.g., WiFi). A path location may be determined or derived from the data comprising any one of satellite data, short-range wireless technology, or wireless network protocols based on the IEEE 802.11 family of standards. A path location may also be obtained or derived from other sources of location information, for example, from a third-party source, for example map data, e.g. from Google Maps, Bing Maps, or Open Maps.

The interpolation locations may be located on a path between the path locations. The path may be a straight line, a curve (e.g., a Bezier curve), or a spline.

The interpolation locations may be determined using data comprising map data. For example, the interpolation locations between two path locations may be located along an existing path comprised within map data, for example, a road, a cycle way, a bridle way, a walking or hiking path, etc., or other known route for which there is associated map data.

The interpolation locations may be determined using motion sensor data. The motion sensor may be one or more of an inertia measuring unit, a gyroscope, or an accelerometer. These data may be used in to determine the path between two known satellite positions using dead reckoning.

The interpolation locations may be determined using data from previous route data.

For example, a user, or a previous user, may have travelled the same or a similar route previously, and these location data could be used to determine the position of the interpolation locations.

The modelled concentration values of the corresponding air pollutant at each of a plurality of model locations may be updated using air pollutant data from a sensor. For example, an air quality model comprising the modelled concentration values of the corresponding air pollutant at each of a plurality of model locations may be an annual model, that is, a model that represents the annual average of the air pollutant at each of the model locations. This annual model may be updated using sensor data from known locations with respect to the model locations. Update may be at any suitable timeframe, for example, monthly, weekly, daily, hourly, every minute, every second or in "real-time", where sensor data update the modelled concentration values of the corresponding air pollutant at each of a plurality of model locations on the fly when the data is received by a processor. The sensor may be at a sensor location. There may be more than one sensor.

The air pollutant data from the sensor may update the modelled concentration values of the corresponding air pollutant at each of a plurality of model locations using a regression of the concentrations against the modelled concentration values, to determine a scale and an offset of the air pollutant concentration to apply to the modelled concentration.

The method may further comprise interpolating scaling factors between live sensor measurements, or extrapolating scaling factors beyond the most recent live measurement, for example, for route planning.

The air pollutants may be selected from the list of: particles with a diameter of 10 pm of less; particles with a diameter of 2.5 pm of less; nitrogen dioxide; and ozone.

The method may further comprise calculating an average, minimum, or maximum concentration of one or more air pollutants for a path.

The method may further comprise calculating a dose of the one or more air pollutants using the concentration profiles of the one or more air pollutants, the exposure duration, and the volume of air inhaled per unit time.

The exposure duration is based on the time spent at each path location or interpolated location. The volume of air inhaled per unit of time may be based on biometric data, for example, from a smart wearable device, or inputted by a user, or may be based on mean or default ventilation rates for an activity type. The dose of the one or more air pollutants may be an average dose, a minimum dose, or a maximum dose. The dose of the one or more air pollutants may be calculated based on a presumed activity rate based on activity type and integrated with biometric data. Heart rate may be used as a proxy for respiration rate.

The method may further comprise comparing the concentration profiles of the one or more air pollutants for two or more routes, the average concentration of one or more air pollutants, or the dose of one or more air pollutants, and presenting the results to a user.

Comparing may comprise calculating the difference between concentration profiles, average concentrations, or doses of the one or more pollutants.

The method may further comprise selecting a preferred route from two or more paths based on the results of the comparison of the two or more routes.

A preferred route may be based on the level of exposure to the one or more pollutants, for example, lowest exposure to PM2.5, or be an overall average of all air pollutants, or it may be a compromise based on user selected preferences for speed or distance in combination with air pollutant exposure. The route may be selected based on a recommended maximum or safe level of exposure to one or more pollutants.

At least two path locations may comprise time information, and the concentration profile of the one or more air pollutants is weighted according to the time information of the at least two path locations.

For example, a path may include staying at some locations for longer than others, e.g., traffic lights, a road crossing, or a particularly congested route. By including time information with the path location, the exposure to one or more of the air pollutants can be calibrated or adjusted to reflect that the different in pollutant exposure.

According to a second aspect of the invention, there is provided a server comprising a processor, the server configured to receive a path comprising a sequence of path locations from a client device, the processor configured to perform the method of the first aspect.

According to a third aspect of the invention, there is provided a mobile device configured to send a sequence of path locations to a server and to receive one or more concentration profiles of air pollutants for that sequence of path locations from the server.

According to a fourth aspect of the invention, there is provided a system comprising: a server comprising a processor; and a mobile device. The mobile device is configured to send a path comprising a sequence of path locations to the server, the server configured to receive the path comprising the sequence of path locations from the mobile device, the processor configured to calculate at least one concentration profile using the method of the first aspect, and the server configured to send the at least one concentration profile to the mobile device.

Brief description of the drawings

Certain embodiments of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which: Figure 1 is a map of Greater London showing annual mean nitrogen dioxide concentrations; Figure 2 is a map of selected streets of London showing annual mean nitrogen dioxide concentrations; Figure 3 is a table of example concentrations of nitrogen dioxide at six different coordinates; Figure 4 is a grid of concentration estimates of an aerial view of an area, each square representing 20 x 20 m; Figure 5 is an orthographic view of a city with a cyclist and their route depicted; Figure 6 is the grid of Figure 4, overlaid with an example cyclist route; Figure 7 is an example of four 20 x 20 m concentration estimate squares with a user's route overlaid; Figure 8 shows the necessary coordinates required for calculating a bilinear interpolation for a concentration at an intermediate point; Figure 9 is a grid of nine 20 x 20 m concentration estimate squares showing the coordinates required for calculating a bilinear interpolation for concentration at an intermediate point; Figure 10 is the grid of Figure 6, with interpolation points between each GPS fix; Figure 11 is an example of how to calculate the position of interpolation points between GPS locations; Figure 12 is the route of Figure 10 subdivided into legs of the route; Figure 13 is a map of London showing two alternative routes from a start location to an end location; Figure 14 is a table of four pollutants and the concentration levels at which they are considered to be safe or not; Figure 15 is a map of streets of London with two alternative routes overlaid; Figure 16 is a table of different ways of calculating the dose of pollutant a user may receive; Figure 17 is a leg of a route with interpolation points between two GPS points; Figure 18 is a process flow diagram for calculating a concentration profile for a pollutant; and Figure 19 is a system block diagram of a system for calculating a concentration profile for a pollutant.

Detailed description of certain embodiments

Theoretical Approach The present invention relates to a system for providing personalized air pollution exposure feedback using a point-based air pollution model. The system described here uses the London Atmospheric Emissions Inventory (LAEI) and ERG's Nowcast system, but it is important to note that the theoretical approach described below is not necessarily dependent on ERG's air pollution model, it could be used with any point-based model that provides estimates at discrete points in space and time, such as UV, temperature, humidity etc., or a different air pollution concentration.

ERG operates a real-time model called a 'Nowcastr, which is based on an annual model (in this case the London Atmospheric Emissions Inventory (LAEI), see https://data.london.gov.uk/air-quality/). The LAEI is produced by ERG's modelling team for the London Mayor's office at two to three year intervals, and provides annual average models of nitrogen dioxide (NO2), ozone (03), particulates with a diameter of 10 pm or less (PM10), and particulates with a diameter of 2.5 pm or less (PM2.5) (the four commonly regulated air pollutants in the UK and globally). The LAEI also produces a range of future models based on a range of predictive scenarios.

Referring to Figure 1, the annual mean nitrogen dioxide (NO2) concentration in pg/m3 from the LAEI model is presented as a grid of 20 x 20 m squares, representing different pollution concentrations for the area of Greater London, is mapped using a colourmap where blue represents low concentrations, green medium, but below a "safe" predetermined limit, and yellow and red represent concentrations above the predetermined "safe" limit. The safe limit is determined by the government's Committee on the Medical Effects of Air Pollutants (COMEAP) review of the UK's air quality guidelines published in 2011 (DEFRA), currently 40 pg/m3. Therefore, in Figure 1, anything over 40 pg/m3 is a "warm" colour (yellow to red). Referring also to Figure 2, the detail of the annual mean NO2 concentration in London, showing high concentrations everywhere in yellow, and very high and extremely high concentrations in red and dark red along the major roads.

Referring to Figure 3, an example of the underlying data used to generate the maps in Figures 1 and 3 comprises Cartesian coordinate data in the form of Easting (x) and Northing (y) grid coordinates, and the associated concentration (conc) for that 20 x 20 m grid square. The LAEI model is presented as a 20 x 20 m grid of squares representing different pollution concentrations across the city. The LAEI model -10 -comprises a grid of point estimates of pollution concentration at the centre of those squares. Each point estimate is derived from a combination of emission sources, meteorological data, and dispersion modelling. The Nowcast model updates these point estimates every hour using real-time monitoring data from over 100 stations across London. The Nowcast model does not interpolate between the points to provide estimates at any location within the grid (https://www.londonair.org.uk/LondonAir/nowcast.aspx), however, as will be described in more detail later, in the present invention, estimates can be calculated for any grid point using interpolation.

Concentration interpolation theory Referring to Figure 4, example concentration point estimates of a pollutant are plotted in a 6 x 6 grid 1 of squares 2, each square 2 representing 20 x 20 m. These point estimates from the LAEI model (or any other point-based model) are used as inputs to calculate personalized air pollution exposure feedback for individual users. Location and activity data from smart devices (e.g., smartphones, smart watches, or a wearable smart device), and, optionally, personal biometric data from wearable devices or user input, and other relevant data sources may be used to adjust the exposure calculation according to the user's characteristics and behaviour. The system then provides the exposure feedback to the user via a mobile application or a web interface. The exposure feedback can include real-time and historical exposure levels, health risks, recommendations, and other information related to air pollution. The system can also provide aggregated exposure feedback for groups of users or populations.

The present invention relates to a method and system for determining the location of a portable device (e.g., a smartphone) using various techniques. One of the most commonly used techniques for tracking the location of a smartphone is the global positioning system (GPS). GPS is a satellite-based navigation system that provides accurate location information to a GPS tracker by comparing the time difference between the signals received from multiple satellites. The GPS tracking device carries a database of the orbital paths of the satellites and uses this information to calculate its position on the earth.

Referring to Figure 5, an orthographic projection of a city block is overlaid with an example trajectory of a user 3 (in this case a cyclist, but the user could be a walker, jogger, or any person who may be exposed to pollution along a route. The user 3 may also be a planner of a route, who may not or may not plan to move along the route themselves). The user 3 is carrying a global positioning system tracking device (e.g., a smartphone, a smartwatch etc.), and periodically receives location fixes 4i, 42, 43, 44, ., 4n which include the latitude, longitude (or other x, y position information), and a time stamp. However, location information 4 could be obtained from other suitable devices, or from route planning.

Using a path comprising the location data, and air pollutant data as shown in Figure 4, it is possible, for a given air pollutant, to determine a concentration profile of the given air pollutant as a function of distance and/or time along the path. Path location data may be either collected via GPS or other suitable method, or input as coordinate data, for example, when used for route planning. Air pollutant data for any suitable pollutant may be used, but particularly particles with a diameter of 10 pm or less, particles with a diameter of 2.5 pm or less, nitrogen dioxide, and ozone.

Obtaining location data from GPS fixes can have some limitations, especially in urban environments where there are many tall buildings and structures that can interfere with the satellite signals. The satellite signals can be lost or deflected by the buildings before they reach the smartphone, resulting in multipath propagation. This means that the smartphone may not receive the signals from enough satellites to determine its location, or it may receive inaccurate signals that cause errors in the location calculation. Therefore, the smartphone may not be able to obtain a GPS lock at a regular interval, as requested by an application, but only sporadically, as it moves in and out of the line of sight of the satellites.

Referring also to Figure 6, consider the case of the cyclist 3 in Figure 5 who is moving along a route in a city. The cyclist's 3 smartphone may obtain a GPS lock 4 at 12:22:52, then at 12:22:55, then at 12:23:10, and then at 12:23:13, as indicated by the location points 4 on the route in Figure 5. However, between these times, the smartphone may not be able to obtain a GPS lock 4, due to the interference of the buildings. This results in gaps in the location information, which may affect the accuracy and reliability of the tracking system. Referring specifically to Figure 6, thirteen location fixes (GPS locks) 4 obtained for the cyclist 3 are plotted along with the example concentrations point estimates as shown in Figure 4, along with a predicted trajectory 5 as a dashed line. Each location 4 has an associated timestamp (not shown). The concentration and distribution of the GPS location fixes 4 may vary over the cyclist's 3 trajectory 5. Therefore, some parts of the trajectory 5 may be represented by location fixes 4 more than others. Interpolating concentration points -12 -along the route may allow for a more accurate calculation of the pollution concentration profile.

Referring to Figure 7, there an example of four concentration point estimates representing 20 x 20 m squares 2 of the grid 1. The concentration point estimates are for Eastings 519160, 519180 and Northings 180140, 180160 with a location point 4 on a user's 3 trajectory 5 overlaid. To obtain the most accurate picture of the user's 3 exposure through air pollutant model domain, the concentration at their GPS lock locations 4 needs to be determined. One way of determining the concentration at the GPS lock locations 4 is to use bilinear interpolation.

Referring to Figure 8, bilinear interpolation is commonly used in continuous maps such as air quality models. The nearest four points of the pollution model are used to interpolate the value of an unknown point. Air quality models such as the LAEI used here, contain features such as roads and junctions where the modelled pollution concentration can be significantly higher than the adjacent pavement or park, for example see Figure 2. For this reason, when interpolating concentrations in this type of model, it is better to use nearby points, thus lessening the influence of further away points. Interpolating may provide the most accurate picture of the concentrations along the route. Here, the GPS point 4 is labelled P, the four nearest points to P are labelled Q12, Q11, Q22, and Q21, the location on the x-axis between Q12 and Q22 is labelled R2, and the location on the x-axis between Q11 and Q21 is labelled RI.

The bilinear interpolation equations are as follows: x -f (x. Yi) 2 - f (Q +x x (Q20 x2 2 X x1 f x2 -x.Y2) = (Qu) F -1(222) X2 X1 X2 X1 Y2 Y Y (x.Y) = -f + -f(x. Y2) Y2 -Y1 Y2 -Y1 Y2 -y x2 -x x -x, Y Y1 ( x2 -x x -x, f (x,Y) f (Q 1) +X2 X1 1(222)) Y2 -Y1 x2 - (Q21)) + Y2 Y1 X2 -XI (Q12) + X2 Xi (4) f (x, Y) = (x2 -x1) (Y2 -) (f(Q21)(x -40,2 -+ (Q 21)(x -xi)(Y2 -+ (Qi2)(x2 -x)(y -3/1) + f (Q22)(x -xi)(Y -Y1) -13 - 1 [x2 x (P12)1[Y 2 -yl (x, y) = (x2 -xi)(372- If (Q21) (Q22)1 11.1 Referring also to Figure 9, in this worked example, the concentrations of the four closest points to P are as follows: Q12 = 81.2, Q22 = 53.2, Q11 = 90.4, Q21 = 80.4. The known coordinates are: X1 = 519180, Y1 = 180060, X2 = 519200, Y2 = 180080 Solve for R1: R1(x, y) = Q11 * (x2 -x) / (x2 -xl) + Q21 * (x -xl) / (x2 -xl) R1(x,y) = ((90.4 * (519200 -519185)) / (519200 -519180)) + ((80.4 * (519185 - 519180)) / (519200 -519180)) = 87.9 R1(x,y) = ((90.4 * (15)) / (20)) + ((80.4 * (5)) / (20)) = 87.9 Solve for R2: R2(x, y) = Q12 * (x2 -x) / (x2 -xl) + Q22 * (x -xl) / (x2 -xl) R2(x, y) = ((81.2 * (519200 -519185)) / (519200 -519180)) + ((53.2 * (519185 - 519180)) / (519200 -519180)) = 74.2 R2(x, y) = ((81.2 * (15)) / (20)) + ((53.2 * (5)) / (20)) = 74.2 Solve for P: P(x, y) = R1 * (y2 -y) / (y2 -yl) + R2 * (y -yl) / (y2 -yl) P(x, y) = ((87.9 * (180080 -180075)) / (180080 -180060)) + ((74.2 * (180075 - 180060)) / (180080 -180060)) = 77.625 Therefore the value of the unknown point 4 is 77.625.

Linear route interpolation Referring to Figure 10, the concentrations of the locations 41, 42, ..., 413, along the trajectory 5 are calculated using the bilinear interpolation method. The average concentration of the route 5 is the sum of the concentrations, C, at each location 4 divided by the number, N, of location points.

RouteAverage =

EC N (7)

-14 -However, using this method, concentration estimates can only be determined for each location 4 along the trajectory 5. For many routes, this may be sufficient, but for some routes, there may be large gaps (e.g., greater than 5 m, or greater than 10 m) between GPS location fixes 4. In such situations, it is possible to interpolate the location (also referred to as interpolated location 6) of the user 3 between the location fixes 4 obtained from the GPS. Performing the interpolation calculation every 1 m for example along the route may allow for the calculation of the average concentration along the route with greater accuracy.

Referring to also Figure 11, the incoming latitude and longitude positions from the device are converted (transformed) to the nearest easting/northing 1 m integer location. The distance between known route points 4 is calculated using Pythagoras. In the following example, Point A is at 519180 easting, and 180080 northing and Point B is at 519187 easting and 180074 northing. From this it is known that Point B is 7 meters east and 6 meters south of Point A. Therefore, it is known that side A of a right-angled triangle is 6m and side B is 7m. Knowing the length of side A and side B of this right-angled triangle, we can calculate the length of side C using Pythagoras.

A2 + B2 = C2 62 + 72= C2 36 + 49 = C2 = C' C2 = V85 C = 9.22 This distance is then split into n equal segments and the location of the interpolated points calculated. In this example, the length, L, of side C is 9.22 m. The distance between each interpolated point will therefore be 9.22/9 = 1.02 m. L-1 interpolation points are generated. In this example eight interpolation points are required. Starting at origin Point A, the position of the points to be interpolated along the hypotenuse C are calculated by either adding or subtracting from the origin X, Y position depending on whether the heading is north-east, north-west, south-east or south-west from the origin position.

In this example the heading is south-east from the starting position. Therefore, iteratively adding from the X starting position to move gradually east, and iteratively subtracting from the Y position to move gradually south. Therefore, for the first interpolated X position, moving east, the length of side B is divided by the length of -15 -side C and added to the origin position. In the example below the first interpolated X position is 519180.76. For the Y position, moving south, the length of side A is divided by the length of side C and subtracted from the origin position. In the example below the first interpolated Y position is 180079.35. This may be performed iteratively, adding and/or subtracting from the previous X, Y position until the required number of interpolations have been performed. This method can then be repeated for the next consecutive pair (or "route pair") of GPS locations 4 along the trajectory 5 until the end of the route 5 is reached.

Time-weighting of the route 5 Referring to Figure 12, as well as changing direction along a route 5, a subject 3 is likely to stop/start and modulate their speed along the course of the route, for example to navigate obstacles, to negotiate traffic, or to stop at road signals. This may mean for example that a subject 3 spends more time in a higher pollution part of the route and less time in a lower pollution part of the route. To get a true picture of the average exposure along a route, the time spent in each part of the route is accounted for. For the time weighting, the GPS lock locations 4 may be used as these are the known points. In between those location fixes 4, and in the absence of any other information regarding speed or direction, a constant speed and direction is assumed. By looking at the GPS lock points 4 along the route, the time spent in different sections 7 (also referred to as a journey "leg") of the route as a proportion of the whole journey time can be determined. The fraction of the overall journey each leg 7 represents can then be determined. By appropriately weighting the average of this leg of the journey, it is then possible to determine the correct time-weighted average of the journey.

The example trajectory 5 in Figure 12 has thirteen GPS location fixes 4i, 42, ..., 413, with twelve legs 7i, 72, ..., 712 between consecutive locations 4. The location fixes have the following timestamps in Table 1:

Table 1

Location fix Timestamp 1 12:22:52 2 12:22:55 3 12:23:10 4 12:23:13 12:23:15 6 12:23:18 -16 -7 12:23:24 8 12:23:29 9 12:23:35 12:23:38 11 12:23:39 12 12:23:42 13 12:23:52 Thus, the journey starts at 12:22:52 and ends at 12:23:52, and the total journey length is 1 minute (60 s). Leg one 7i starts at 12:22:52 and ends at 12:22:55, therefore leg one 71 takes 3 seconds. Therefore, leg one 71. represents (3/60) x 100 = 5% of the total journey length.

As a proportion, the legs 7 represent:] * Leg 1 = (3/60) = 0.05 * Leg 2 = (15/60) = 0.25 * Leg 3 = (3/60) = 0.05 * Leg 4 = (2/60) = 0.03 * Leg 5 = (3/60) = 0.05 * Leg 6 = (6/60) = 0.1 * Leg 7 = (5/60) = 0.08 * Leg 8 = (6/60) = 0.1 * Leg 9 = (3/60) = 0.05 * Leg 10 = (1/60) = 0.016 * Leg 11 = (3/60) = 0.05 * Leg 12 = (10/60) = 0.16 The average concentration of each of the legs 7 is known from the concentration of the start point and end point and every interpolated point in-between. To properly time weight the journey, the average concentration of the leg is multiplied by the decimal fraction of the total journey length it represents. This gives the Time Weighted Average (TWA) for each leg: * Legl TWA = (65 pg/m3* 0.05) = 3.25 pg/m3 * Leg2 TWA = (43 pg/m3* 0.25) = 10.75 pg/m3 * Leg 3 TWA = (22 pg/m3* 0.05) = 1.1 pg/m3 * Leg4 TWA = (14 pg/m3* 0.03) = 0.42 pg/m3 -17 - * LegS TWA = (51 pg/m3* 0.05) = 2.55 pg/m3 * Leg6 TWA = (48 pg/m3* 0.1) = 4.8 pg/m3 * Leg7 TWA = (34 pg/m3* 0.08) = 2.72 pg/m3 * Leg8 TWA = (16 pg/m3* 0.1) = 1.6 pg/m3 * Leg9 TWA = (42 pg/m3* 0.05) = 2.1 pg/m3 * Leg10 TWA = (31 pg/m3* 0.016) = 0.496 pg/m3 * Legll TWA = (67 pg/m3* 0.05) = 3.35 pg/m3 * Leg 12 TWA = (14 pg/m3* 0.16) = 2.24 pg/m3 To get the TWA for the whole journey, the sum of the TWAs for all the legs 7 is calculated.

TWARoute = TWALegs (8) The TWA for this journey is therefore: (3.25+10.75+1.1+0.42+2.55+4.8+2.72+1.6+2.1+0.496+3.35+2.24) =35.37 pg/m3.

By performing a combination of 1 m concentration interpolations along the route and weighting the average of the route by time fraction of journey legs it is possible to arrive at best possible average for the route from the available data. For example, if a route is 1km long, 1,000 1 m interpolations may be performed. If that route has 100 GPS lock 4 locations it is possible to perform 99 time-weighting leg 7 calculations for those GPS location 4. In the present method, this is performed for each pollutant model NO2, PM10, PM2.5, and 03. Calculating the TWA exposure for a 1 km journey for all four pollutants therefore may therefore involve thousands of calculations.

Real-time model The above approach can be applied to an air quality model of any type i.e., annual model or daily model or hourly model. The above approach may be applied to any type of point model, for example, pollen, temperature, ultraviolet exposure, etc. In the present approach a TWA in pg/m3 is calculated for the route from the base annual model for each pollutant of interest. Imperial College's Environmental Research Group creates a real-time model by collecting real-time NO2, PM10, PM2.5 and 03 from all the monitoring stations across London Air Quality Network and running a regression of these concentrations against the annual averages of the concentrations from the -18 -monitoring stations of the year of the model. This provides a scale and offset for each pollutant and may allow the scaling of the annual map up or down to reflect the current conditions more accurately. Such scaling can be performed periodically, for example every day, every hour, every 10 minutes, or every minute, depending on the temporal resolution desired.

From these regressions, a scale and offset for each pollutant is calculated. For example: * NO2 -The scale is 0.639 and the offset is -11.9 * 03 -The scale is 1.1 and the offset -25.7 * PM10 -The scale is 1.5 and the offset is -18.6 * PM2.5 -The scale is 1 and the offset is -10.5 By multiplying the TWA of the route derived from the annual or 'base' map by the real-time scale and offset it is possible to derive a real-time average for the route for each pollutant. In the example above the TWA of the route was 35.37 pg/m3. By multiplying the TWA by the real-time scale and adding the offset for the pollutant in question, it is possible to derive the current real-time average of the route 5.

TWARouteRealtime = (TWARoute * Nowcast Scale) + (Offset) TWARouteRealtime = (35.37 * 0.639) + (-11.9) = 10.7 ug/m3 As the scale and offset for the real-time map is the same for the whole map, these can also be applied to individual point queries. If, for example, a user 3 wanted to know what the current modelled concentration for NO2 was at a particular latitude/longitude, it is possible to derive the annual concentration using the bilinear interpolation approach described above, then multiply that result by the current scale and offset to provide the real-time concentration.

The Nowcast scale and offset multiplication can be performed on each interpolated point 6 along the route at the same time the 'base' or annual interpolation is calculated. This can provide more flexibility, for example it may allow for a user to assess sections of the route in isolation. If the Nowcast multiplication was performed for the entire route only it wouldn't allow us to interrogate real-time values along the route. Thus, for a 1 km route, 1,000 1 m interpolation calculations are performed, plus 1,000 Nowcast multiplications, plus however many route leg calculations are required for each pollutant.

-19 -For a 1 km route, to calculate the average annual and real-time concentrations of a given pollutant, (e.g., NO2, PM10, PM2.5 and 03 concentrations) may require, for example, 2,000 interpolation and multiplication calculations (if there is just a start and end point and therefore only 1 journey leg).

The annual or current map can be generated or acquired in a variety of different ways. For example, different sorts of data could be included, for example, weather, traffic, point sources etc. The result of the above calculations is an annual and/or real-time model which is a grid of pollution concentrations. It also doesn't matter what resolution the grid is, it could be 20 m, S m, 1 m, 1 km.

Inter-hour interpolation The Nowcast factors can be produced every hour and can be applied to scaling the baseline annual concentrations in that hour, i.e., a Nowcast factor for 17:00 applies from 17:00-17:59. New Nowcast factors are received at 18:00. Air pollution concentrations change continually, moving up and down. For example, a scale and offset for NO2 for 17:00 may be (0.5) + (-1), then the scale and offset for 18:00 may be (1) + (-0.5). This tells us that the concentration of NO2 has increased from the 17:00 reading to the 18:00 reading.

The real pollution levels may have gone up and down during the hour of course, they will not have necessarily increased (or decreased) linearly across the hour. However, as with the interpolations between the GPS lock points 4, in the absence of any other information, a linear change between the two known data points is assumed. Where the exposure of a route that starts at say 17:15 and finishes at 17:45 is calculated, as the concentrations of NO2 have been rising across the hour, the person 3 will likely have been exposed to higher ambient concentrations towards the end of their journey than at the start.

To better reflect this in the calculation, it is possible to interpolate a scale plus offset factor for each minute between the 17:00 and 18:00 hours (or indeed each second).

For example, consider the following example sample movement data in Table 2:

Table 2

Mode Longitude Latitude Timestamp Cycling -0.1279713396052742 51.56388094754018 2020-05- 12T17: 15: 00Z -20 -Cycling -0.1281296814121595 51.56378823247811 2020-05-12T 17:30:007 Cycling -0.12828975328695036 51.56369229755106 2020-05- 12T07:45:00Z There is a GPS lock location 4 at 17:15, one at 17:30 and one at 17:45. The 17:00 Nowcast factors are (0.5) + (-1), the 18:00 Nowcast factors are (1) + (-0.5). The first data point is 17:15 -a quarter (0.25) of the way through the hour. Therefore, it is possible to apply an interpolated scaling factor of 0.625 between (0.5) and (1).

To do this, the hour starting factor may be defined as X and the hour ending factor is defined as Y. The fraction the minutes and/or seconds represent of the hour is defined as FIH. It is possible to define the product of this equation as Z: (Y -X)* FIN = Z (9) Where FIH is a proportion of the hour concerned. In this example Z = (1-0.5)*0.25= 0.125 The Interpolated Scaling Factor (ISF) then is considered the starting factor plus Z ISF = X + Z (10) Thus: ISF = 0.5 + 0.125 ISF = 0.625 The same calculation can be performed while including the offset to determine an interpolated offset figure.

In this example the product of this equation is defined as B. B = ((-1) -(-0.5))*0.25 = -0.125 The interpolated offset (I0) is then the starting offset (A) plus (B): /0 = A + B Thus: IO = -1 + -0.125 IO = -1.125 -21 -This interpolated scaling factor can then be used to determine the real-time concentration of the 17:15:00 point. For example, if the baseline (annual) concentration for the 17:15:00 point is 52 pg/m3, the real-time concentration is (52 * 0.625) + (-1.125) = 31.375 pg/m3.

This principle may be applied to all interpolated concentration points for the route across the hour ensuring the calculation of the most accurate real-time concentrations for the route possible from the available data.

Datamap file As described above, calculating the annual and real-time TWA for a 1km route for all four pollutants (NO2, 03, PM10, PM2.5) requires many thousands of calculations. If an application (app) is sending location and movement data to a service whilst it runs in the background of an operating system, its rights are limited and the window of opportunity for sending data to a service and receiving the return may be a maximum of 30 seconds, but could be significantly shorter (for example, see https://developer.apple. com/documentation/backgroundtasks/choosing_background_s trategies for your app). Therefore, the system needs to be able to perform thousands of calculations and return the result back to the app quickly. To achieve this, a new file type called a.datamap was devised.

A.datamap file holds the annual model concentration data as binary values in a grid format. The header of the file holds meta information about the file including its dimensions i.e., how many rows and columns it has and the X Easting and Y Northing of the origin concentration point at location 0,0. Referring again to Figure 3, example source data comprising x (Easting), y (Northing), and conc (Concentration) for six locations is displayed.

This source data can be transferred into a bespoke.datamap file using a Python script (or other suitable language script) which takes the source file (a comma separated values file -.csv) and copies the concentrations (also referred to as "stripped out". It is possible for the script to copy the concentration values to 2 decimal points to save file space. Each concentration number may then be converted to binary and the concentrations are stored sequentially in the.datamap file. Two bytes allows storing a binary value in the range 0-65535. Splitting a floating point value into the whole number and fraction and scaling the fraction part in range 0..<1 to be represented by the range 0..<65536 allows storing a floating point value in four bytes. For example, -22 - 51.64 would be stored as 51 in first two bytes and 65536 * .64 in the second two bytes. 51 is 0033 and 65536 * .64 = 41943 or a3d7 hexadecimal. The 4 bytes thus being 0033a3d7. The result is a file which contains all the concentrations for the model in a 2-dimensional array.

An incoming request to the file for a concentration at an Easting/Northing location can seek to the correct concentration by referring to the meta information in the file header and using an equation. For example, the originX and originY in an example file is 519100, 203440. The source format of the file is a 20 m grid. Therefore, each point is 20 m from each other. The file has 1,000 columns across and 1,000 rows down. To seek to the location for the concentration at point 519020, 203360 (80 m east and 80 m south of the file origin) the following equation may be used: SeekLocation = ((x_origin -x) * 4) + ((y_origin -y) * 4 * x_width) -I-file_header_size The file header size is where the meta data about the origin and dimensions is held. Therefore, this may be added on to the equation to ensure the seek head arrives at the correct location. The file header size in this example is 16 bytes. The 4 is because each concentration is held as 4 bytes so the read head may be sent to the end of the byte package and read 4 bytes backwards.

Thus, the SeekLocation is: SeekLocation = ((x origin -x) * 4) + ((y origin -y) * 4 * x width) + file header size SeekLocation = ((519100 -519020) * 4) + ((203440 -203360) * 4 * 1000) + 16 SeekLocation = (80 * 4) + (80 * 4 * 1000) + 16 SeekLocation = (320) + (320,000) + 16 SeekLocation = 320336 The resulting number tells the file read head where to locate the concentration required. Using this file format means concentration retrieval time is constant no matter where the concentration is held in the file and no matter how big the file is. This makes it very fast and very efficient way of storing and retrieving concentrations for use in the route calculations. A.datamap file may be generated for each pollutant (NO2, PM10, PM2.5, 03) . Fractional Average -23 -Time-weighting the average exposure of a person along a route using the model is only possible once the user 3 has completed the journey, that is, once the user 3 has completed their journey their movement data may be collected and analysed. However, knowledge of the average pollution along one or more routes "live" (i.e., on demand) or even in the future with no movement information can be useful for route planning, for example, if a user 3 wanted to plan a route minimising exposure to one or more pollutants.

If a user 3 queries for the directions between a start point and an end point, an online mapping tool (e.g., Google maps, Bing, OpenStreetMap, etc. along with many other mapping systems) can return, one or more alternative routes between the start and end points. The returned route(s) will include latitude/longitude points along the route(s) where direction changes and an expected journey duration. When calculating pollution exposure estimates for this or these route(s), it may not be possible to calculate the time-weighted average (TWA) exposure in the same way as described earlier, thus, a constant speed along the route(s) may be assumed. Alternatively, traffic data specific to that mode of transport, or historical movement data either from the user 3 or from different users with the same or similar modes of transport may be used to calculate a weighting coefficient to be applied to the pollution profile estimates.

Referring to Figure 13, faced with these options, a user 3 may want to compare the pollution difference between the one or more routes. Consider the two potential walking routes between Leicester Square and Holborn. The two routes are of a similar distance -route A one 0.7 miles / 14 minutes -and route B 0.6miles / 13 minutes.

Using the latitude/longitude arrays which describe the routes, and using the method described above, it is possible to calculate the annual average pollution concentration from the base map and the real-time pollution concentration from the Nowcast scaling values along each route for all four pollutants (NO2, 03, PM10, PM2.5) Suppose that the average pollution concentrations for the routes were this: Pollutant Average A Route B Route NO2 20 pg/m3 10 pg/m3 03 50 pg/m3 50 pg/m3 PM10 25 pg/m3 25 pg/m3 PM2.5 10 pg/m3 20 pg/m3 -24 -The 03 and PM10 averages are the same for each route. The A route has an NO2 average of 20 pg/m3 and a PM2.5 average of 10 pg/m3. The B route has the opposite a PM2.5 concentration of 20 pg/m3 and an NO2 average of pg/m3. However, these two routes are not equally polluted because not all pollutants are equally harmful to health at the same concentration. Referring to Figure 14 the UK's Daily Air Quality Index, set the four pollutants against a 1-10 scale but they each have different ranges.

For example, level 10 for NO2 is 601 pg/m3 whereas for PM2.5 it is only 71 pg/m3. To fairly compare the average concentrations along two or more routes, the averages of the different pollutants along a route are normalised or calibrated according to this scale.

Real-time fractional average calculations The current Daily Air Quality Index is from the government's Committee on the Medical Effects of Air Pollutants (COMEAP) review of the UK's air quality guidelines published in 2011 (DEFRA). The report notes that the index is based on the World Health Organisation 2006 air quality short term guidelines with two noted deviations on 03 where the committee felt a lower breakpoint was warranted and on PM2.5 where a higher breakpoint warranted due to the higher ratio of PM2.5/PM10 in the UK.

The WHO short term guidelines can be found on P175 of the WHO Air Quality Guidelines Global update 2005 (WHO, 2006). Taking the approach that the UK index is based on the low/moderate breakpoint and the rest of the index levels spread from that, that provides a basis by which to compare average concentrations more fairly across the four pollutants.

If the moderate breakpoint for each pollutant is set as one, it is possible to then calculate a "fractional average" by multiplying the average concentration calculated from a route by the moderate breakpoint value. For example, taking the A and B routes above, the NO2 concentration of route A is 20 pg/m3. The breakpoint for moderate NO2 from the index is 201 pg/m3. Therefore, the fractional average concentration of NO2 on the route is (20/201) = 0.1. On the B route the NO2 average was 10 pg/m3, meaning the fractional average is (10/201) = 0.05. On the A route, the PM2.5 average was 10 pg/m3. Meaning the fractional average was (10/36) = 0.27. On the B route, the PM2.5 average was 20 pg/m3, meaning the fractional average was (20/36) = 0.55. The PM10 and 03 averages along both routes were the same. If the fractional averages of the NO2 and PM2.5 from the A route are summed, the result is: (0.1 + 0.27) = 0.37. If the fractional average of the NO2 and PM2.5 on the B route are summed, the result is (0.05 + 0.55) = 0.6. Thus, the higher PM2.5 average on the B -25 -route means that this is the 'more polluted' route than the A route. Therefore, the user 3 may chose route A to reduce their pollution exposure.

Referring to Figure 15, the figure shows how average in pg/m3 can be returned for a route as well as annual and real-time fractional averages. For journeys done in the past where there are timestamped GPS locks 4, the fractional average for the route can be calculated after the calculation of the TWA of the route first using interpolation and journey leg/time weighting. Because concentration points are interpolated every 1 m along the route, it is also possible to calculate a fractional average every 1 m along the route. Alternatively, intermediate averages may be calculated to a more manageable route segment such as 10 m, 20 m etc. This can be useful in fairly comparing how the sum of the four pollutants changes along two or more routes.

Annual fractional average calculations The annual pollution map and the real-time Nowcast factors can be used to return an annual and real-time fractional average for each route. For fractional averages calculated from the annual map, the annual average target values are used to do the normalization (e.g., see the UK national air quality objectives 2023 -https://ukair.defra.gov.uk/assets/documents/Air Quality Objectives Update 20230403.pdf). Dose

Fractional average is a useful way of fairly comparing multiple pollutant averages between two or more routes. But if one route is significantly longer than the other, or one route was walked and the other cycled, the dose of pollutants inhaled needs to be considered. Inhaled air pollution dose can be calculated using the following equation: Dose=C.T*V (11) Where C is the air concentration of aerosol particles or gas, T is the exposure duration (time), and V is the volume of air inhaled per unit time (ventilation rate) (from Introduction to Air Pollution Science: A Public Health Perspective, Robert F Phalen, 2013). Inhaled dose along a route may be different depending on whether the person is walking, running or cycling (basically the intensity of physical activity). As described earlier, it is possible to calculate the average concentration along the route from the GPS/Movement data from the phone (or watch or band or other suitable portable device).

-26 -Using activity data such as whether the person was walking/cycling/running/in a vehicle, it is possible to calculate the inhaled dose along a route. If there is no measured movement data, it is possible to take a generic approach where a general ventilation rate for walking/cycling/running/at rest is used. As described above, route legs 7 from the GPS lock locations 4 are generated along the route. The start and end time of each leg 7 allow for the calculation of the time (T) in seconds of each leg 7. Interpolating in-between the route leg points allows the calculation of the time (T) taken to travel along every sub-divided section of the route. Using the start concentration and end concentration every 1 m along the route, it is possible to calculate an average concentration (C) for every 1 m. It is further possible to use the time taken to travel this 1 m distance (T) and either use a default ventilation rate or ventilation rate calculated from biometric data (V) to calculate the dose every 1 m along the route.

Referring again to Figure 12, the first leg's 7 real-world GPS locks 4 have a timestamp of 12:22:52:00 (hundredths of a second) and the last GPS lock is at 12: 22: 55: 00. For example, if the interpolated concentration of the first point GPS lock point 4 is 66 pg/m3 and the interpolated concentration of the first 1 m interpolated point is 68.4 pg/m3, then the average concentration then for this 1 m segment is (66 + 68.4)/2 = 67.2 pg/m3. The start time of the first GPS lock point 4 is 12:22:52:00. The interpolated timestamp of the first 1 m interpolation point is 12:22:52:60. This means the time taken to travel across this 1 m segment is 60 centiseconds (hundreths of a second) or 600 milliseconds or 0.01 of a minute (time (T)). In this example, the person is cycling, and there is no biometric data for this example so a default ventilation rate of 42.5 L /minute or 0.0425 m3/minute for cycling is used. This is the ventilation rate (V). Therefore, using equation 11, the inhaled dose for this 1 m segment is: Dose = 67.2 * 0.01 * 0.0425 Dose = 0.02856 ug This dose calculation is performed for annual and real-time concentrations for all pollutants along the whole route. For a 1 km route, this would result in 1,000 dose calculations for each pollutant. However, this calculation can also be averaged up across larger segments of the route. For every 5 m, or 10 m for example. Once the dose calculation has been performed for each 1 m segment, a "fractional dose" calculation can also be performed for fairly comparing routes with each other as described above.

-27 -Fractional Dose As with "fractional average", to more fairly compare the pollution exposure difference between one or more routes which may be of different lengths (and therefore have different journey times) or comparing one route which was cycled vs a route which was walked for example, the same fractional approach to the dose calculation is performed as with the averages.

To calculate fractional dose, concentration in equation 11 is replaced with fractional average. In the fractional average example above, the fractional average of the NO2 on route B was 0.05. If the route is four minutes long and the person is cycling, then the fractional dose calculation is: fractional dose = 0.05 * 4 * 0.0425 - fractional dose = 0.0085 Like fractional average, this is a dimensionless number, but it provides a way of fairly comparing inhaled dose of the 4 main pollutants along the route. This calculation is performed for both annual and real-time concentrations every 1 m along the route.

Dose calculation with no biometric data In the case where a route or routes are sent to the service with no biometric data i.e., only a latitude/longitude array describing the route either timestamped or a total journey time for the route and a mode of travel e.g., walking/cycling/running, it is possible to calculate the dose using a generic ventilation rate for each mode.

For example, consider the routes below, they include latitude/longitude pairs, the total journey time and the mode. It is possible to calculate the average pollution concentration along the route using the method described above. The result of this is microgram mes per metre cubed of air pg/m3.

A metre cubed of air is 1,000 litres. The journey time is provided in minutes. Therefore, if a person's minute ventilation rate in litres per minute is known, it is possible to calculate the inhaled dose in pg. In this example, the average concentration along the route is 51.64 pg/m3. The duration is four minutes, and the ventilation rate is 12 litres/minute (divide by 1000 to get to m3/minute).

-28 -Dose = Concentration ((pg/m3) * Time (minutes) * Ventilation Rate ((litres/minute)) / 1000 Dose = ((51.64)* (4) * (12)) /1000 = 2.47 pg Thus, if no ventilation rate is supplied it is possible to use a generic rate for walking/cycling/running. These are: Cycling = 42.5 /minute or 0.0425 m3/min Walking = 22.8 litres/minute or 0.0228 m3/min Running = 79.1 litres/minute or 0.0791 m3/minute These rates are from the World Health Organisation HEAT tool (https://www.who.int/europe/tools-and-tool kits/health -economic-assess ment-tool-forwalking-and-cycling).

Dose calculation (with biometric data) When biometric data is available, it is possible to calculate an inhaled dose along the route which is more accurate/specific to the individual. It is difficult to measure ventilation rate (breathing rate) directly, so a proxy may be used, such as heart rate for physical exertion, and therefore breathing rate. Referring to Figure 16, there are some other biometric factors to glean from the person to help calculate inhaled dose. Figure 17 shows a summary of the dose equations considered and their source.

The most suitable dose equation was: VR = 10[938 x (FIR -IIR yest.)+ 4.22 x height + 1.19 x weight + 2.22 x age +TIR_resti x10-3 -0.0439 (12) Where: VR is Ventilation Rate (litres/minute) HR -Heart rate (beats/min (bpm)) HR rest -Heart rate at rest (beats/min) Height (cm) Weight (kg) Age (years) The equation is from Satoh, T.; Higashi, T.; Sakurai, H.; Omae, K., Development of a new exposure monitoring system considering pulmonary ventilation (DEM 1). The Keio Journal of Medicine 1989, 38, (4), 432-42.

-29 -See formula 3.3 in Figure 16.

The following is a worked example using the following biometric factors: Age -55 years Weight -69.5 Kg Resting HR -51 bpm Height -172 cm Heart Rate -80 bpm VR(1/min) = 10(9.38. (80-51) + 4.22 x 172 + 1.19 x 69.5 + 2.22 x 55 + 51) x 10-3 -0.0439 = 10(9.38 (80-51) + 4.22 x 172 + 1.19 x 69.5 + 2.22 x 55 + 51) x 0.001 -0.0439 = 101253.665 x 0.001 -0.0439 10(1.209765) = 6.714 Thus, the ventilation rate (also known as minute ventilation or tidal volume) from the above example here is 6.7 1/min. Since the ventilation rate (VR) is returned as l/min, dividing the result by 1000 to get to m3/min so all units are equal. VR(m3/min) = 20 0.006714.

Dose calculation can play an important role in understanding the relationship between air pollution exposure and health impacts. By considering factors such as physical activity and ventilation rates, a more accurate exposure-response relationships can be established. Incorporating biometric data, particularly heart rate, as a proxy for breathing rate, enhances the precision of dose calculations. The selection of a suitable equation for dose calculation involved a thorough review of relevant literature and validation using example input data, ultimately leading to the adoption of a method that provided satisfactory outputs. The above equation is suitable for the following reasons: The types of biometric data used in this calculation (height, weight, age, resting heart rate and heart rate) are easily obtained.

The exposure calculation service accepts these biometric data to perform dose calculations if supplied.

Calculating inhaled dose of pollutants along a journey not only allows us a more accurate picture of exposure on that journey but is also important in -30 -fairly comparing the pollution exposure between two or more routes of differing activities.

Heart rate interpolation It is also possible to interpolate heart rate data where heart rate data is recorded at a different frequency to the GPS lock 4 points. Heart rate may be interpolated at the points where interpolated track points are calculated. If heart rate at a first location 4 is 88 bpm and at the following location 4 it is 95 bpm, a linear interpolation between the known heart rate points can provide a more actuate picture of variation in heart rate along the route.

Referring to Figure 17, first and second location points 41, 42 define a first leg 7, and five 1 m interpolation points 101, 102, 103, 104, 105 are interposed between the first and second location points, with sub-legs 11 between each adjacent location point 4 and the interpolation points 10. Heart rate data points may be different to GPS lock points 4. Heart rate data does not necessarily contain or comprise lat/long information (in fact may well not) instead, heart rate points can be 'attached' to the route by their timestamp. Interpolated heart rates can then be generated every 1 m along the route as the interpolated 1 m location points are generated. In the above example, a heart rate reading of 88 bpm timestamped at 12:22:52:60 is received. At this timepoint the user 3 was at the first interpolated 1 m location point 101. The second heart rate reading received is 94 bpm timestamped at 12:22:54:40. At this timepoint, the user was at the fourth interpolated 1 m point 104.

In between the first and fourth interpolated points 10, there are the second and third interpolated points 10. It is therefore possible to linearly interpolate a heart rate at each of those interpolated location points assigning a bpm of 90 bpm to the second interpolated location point 102 and a bpm of 92 bpm to the third interpolated position point 103 in this leg 7. The example given here is linearly interpolating a heart rate within a journey leg 7. Of course, real world heart rate data point may stretch across legs. It is possible to use the heart rates at the received GPS location 4 and the interpolated locations 10 to calculate dose and fractional dose for every 1 m along the route 5 to give the best possible picture of how inhaled dose varies along the route.

Taken together, the above system allows for sophisticated calculations of real-time and annual averages, fractional averages, dose and fractional dose of pollution along routes using either theoretical 'future' routes or real-world location and biometric data for routes or journeys in the past. Even for short routes of 1km or 2km, there are -31 -many thousands of calculations to perform. As described these calculations must be performed and returned back to the phone in seconds.

Referring to Figure 18, using the methods detailed above, it is possible to generate and output or store a concentration profile for a given pollutant for either a proposed route 5, or a route that has been taken by a user 3. Thus, a user's 3 exposure to air pollutants can be calculated. First, a path comprising a sequence of path locations 4 is received (step S1). In step 2, (S2), concentration maps corresponding to one or more air pollutants (e.g., NO2, 03, PM2.5, or PM10) are received or retrieved, where each concentration map comprises modelled concentration values of the corresponding air pollutant at each of a plurality of model locations. At step 3 (S3) the distance between sequential target locations is determined. At step 4 (S4), if a pair of sequential path locations are separated by more than a target spacing (e.g., 1 m), a number of interpolation locations required to meet the target spacing is determined (step 55), and then the required number of interpolation locations between that pair of path locations are inserted (step S6), so every section of the path longer than the target spacing includes at least one path location or interpolation location. Once these interpolation locations have been inserted, or if the sequential path locations 4 were separated by less than the target spacing, at step 7 (57) for each interpolation location and each path location, a concentration value corresponding to that interpolation location or path location based on modelled concentration values of the two or more model locations closest to that interpolation location or path location is interpolated. The concentration profiles of the one or more air pollutants are stored or outputted at step 8 (S8). The process may be performed for any number of pollutants for which concentration maps are available.

Referring to Figure 19, the method described above may be performed on a server 20 comprising a processor 21. The server may receive location or path data 22 comprising a sequence of path locations 4 from a portable device 23, for example, a mobile phone (e.g., a smartphone), a smartwatch, or other suitable device. The device may have a global positioning module (not shown) for receiving GPS location fixes. The server 20 may also receive biometric data 24 from the portable device. The server 20 can receive or retrieve concentration maps corresponding to one or more air pollutants from a database 25 hosted on a database server 26. The processor 21 processes the location data 22, the concentration map data using the method described above to output a concentration profile of the one or more air pollutants. The concentration profile may be outputted to the portable device 23.

-32 -Modifications It will be appreciated that various modifications may be made to the embodiments hereinbefore described. Such modifications may involve equivalent and other features which are already known in the design, configuration and use of systems and methods for calculating concentration profiles for one or more pollutants and component parts thereof and which may be used instead of or in addition to features already described herein. Features of one embodiment may be replaced or supplemented by features of another embodiment.

Although claims have been formulated in this application to particular combinations of features, it should be understood that the scope of the disclosure of the present invention also includes any novel features or any novel combination of features disclosed herein either explicitly or implicitly or any generalization thereof, whether or not it relates to the same invention as presently claimed in any claim and whether or not it mitigates any or all of the same technical problems as does the present invention. The applicants hereby give notice that new claims may be formulated to such features and/or combinations of such features during the prosecution of the present application or of any further application derived therefrom.

Claims (20)

1. -33 -Claims 1. A method of calculating exposure to air pollutants comprising: receiving a path comprising a sequence of path locations; receiving or retrieving concentration maps corresponding to one or more air pollutants, each concentration map comprising modelled concentration values of the corresponding air pollutant at each of a plurality of model locations; for each given air pollutant, determining a concentration profile of the given air pollutant as a function of distance along the path by: in response to a pair of sequential path locations are separated by more than a target spacing, inserting one or more interpolation locations between that pair of path locations, so every section of the path longer than the target spacing includes at least one path location or interpolation location; for each interpolation location and each path location, interpolating a concentration value corresponding to that interpolation location or path location based on modelled concentration values of the two or more model locations closest to that interpolation location or path location; storing or outputting the concentration profiles of the one or more air pollutants.
2. 2. The method of claim 1, wherein the concentration value is interpolated using a time-weighted average between each path location.
3. 3. The method of claim 1 or 2, wherein the concentration value is interpolated using bilinear interpolation of the four closest model locations to each interpolation location or path location.
4. 4. The method of any of claims 1 to 3, wherein the path locations and/or the interpolation locations comprise longitude and latitude.
5. 5. The method of any of claims 1 to 4 wherein the path locations are determined from data comprising satellite data.
6. 6. The method of any of claims 1 to 5 wherein the interpolation locations are located on a path between the path locations.
7. 7. The method of claim 6 wherein the interpolation locations are determined using data comprising map data.
8. -34 - 8. The method of any of claims 1 to 7 wherein the interpolation locations are determined using motion sensor data.
9. 9. The method of any of claims 1 to 8 wherein the interpolation locations are determined using data from previous route data.
10. 10. The method of any of claims 1 to 9, wherein the modelled concentration values of the corresponding air pollutant at each of a plurality of model locations are updated using air pollutant data from a sensor.
11. 11. The method of claim 10, wherein the air pollutant data from the sensor updates the modelled concentration values of the corresponding air pollutant at each of a plurality of model locations using a regression of the concentrations against the modelled concentration values, to determine a scale and an offset of the air pollutant concentration to apply to the modelled concentration.
12. 12. The method of any of claims 1 to 10, wherein the air pollutants are selected from the list of: particles with a diameter of 10 pm of less; particles with a diameter of 2.5 pm of less; nitrogen dioxide; and ozone.
13. 13. The method of any of claims 1 to 12, further comprising calculating an average, minimum, or maximum concentration of one or more air pollutants for a path.
14. 14. The method of any of claims 1 to 13, further comprising calculating a dose of the one or more air pollutants using the concentration profiles of the one or more air pollutants, the exposure duration, and the volume of air inhaled per unit time.
15. 15. The method of any of claims 1 to 14, further comprising comparing the concentration profiles of the one or more air pollutants for two or more routes, the average concentration of one or more air pollutants, or the dose of one or more air pollutants; and presenting the results to a user.
16. -35 - 16. The method of claim 15, further comprising selecting a preferred route from two or more paths based on the results of the comparison of the two or more routes.
17. 17. The method of any of claims 1 to 16 wherein at least two path locations comprise time information, and the concentration profile of the one or more air pollutants is weighted according to the time information of the at least two path locations.
18. 18. A server comprising a processor, the server configured to receive a path comprising a sequence of path locations from a client device, the processor configured to perform the method of any of claims 1 to 17.
19. 19. A mobile device configured to send a sequence of path locations to a server and to receive one or more concentration profiles of air pollutants for that sequence of path locations from the server.
20. 20. A system comprising: a server comprising a processor; and a mobile device; the mobile device configured to send a path comprising a sequence of path locations to the server, the server configured to receive the path comprising the sequence of path locations from the mobile device, the processor configured to calculate at least one concentration profile using the method of any of claims 1 to 17, and the server configured to send the at least one concentration profile to the mobile device.