# Exploring Non-Exhaust Emission Factors

#### 2024-12-02

When assessing vehicle emissions inventories for particles, one relevant step is taking into account the non-exhaust processes, such as tire, brake and road wear. The `gtfs2emis` incorporates the non-exhaust emissions methods from EMEP-EEA.

The following equation is employed to evaluate emissions originating from tire and brake wear

\[ TE_i = dist \times EF_{tsp}(j) \times mf_s(i) \times SC(speed) \] where:

- \(TE(i)\) = total emissions of pollutant \(i\) (g),
- \(dist\) = distance driven by each vehicle (km),
- \(EF_{tsp}(j)\) = TSP (Total Suspended Particle) mass emission factor for vehicles of category \(j\) (g/km),
- \(mf_s(i)\) = mass fraction of TSP that can be attributed to pollutant \(i\),
- \(SC(speed)\) = correction factor for a mean vehicle travelling at a given speed (-).

## Tire

In the case of heavy-duty vehicles, the emission factor needs the incorporation of vehicle size, as determined by the number of axles, and load. These parameters are introduced into the equation as follows:

\[EFTSP^{hdv}_{tire} = 0.5 \times N_{axle} \times LCF_{tire} \times EFTSP^{pc}_{tire}\]

where:

- \(EFTSP^{hdv}_{tire}\) = TSP emission factor for tire wear from heavy-duty vehicles (g/km),
- \(N_{axle}\) = number of vehicle axles (-),
- \(LCF_{tire}\) = a load correction factor for tire wear (-),
- \(EFTSP^{pc}_{tire}\) = TSP emission factor for tire wear from passenger car vehicles (g/km).

and \[LCF_{tire} = 1.41 + (1.38 \times LF)\]

where:

- \(LF\) = load factor (-), ranging from 0 for an empty bus to 1 for a fully laden one.

The function considers the following look-up table for number of vehicle axes:

vehicle class (j) | number of axes
--- | ---
Ubus Midi <=15 t | 2
Ubus Std 15 - 18 t | 2
Ubus Artic >18 t | 3
Coaches Std <=18 t | 2
Coaches Artic >18 t | 3

The size distribution of tire wear particles are given by:

particle size class (i) | mass fraction of TSP
--- | ---
TSP | 1.000
PM10 | 0.600
PM2.5 | 0.420
PM1.0 | 0.060
PM0.1 | 0.048

Finally, the speed correction is:

- \(SC_{tire}(speed) = 1.39\), when \(speed < 40 km/h\);
- \(SC_{tire}(speed) = -0.00974 \times speed + 1.78\), when \(40 <= speed <= 90 km/h\);
- \(SC_{tire}(speed) = 0.902\), when \(speed > 90 km/h\).

    library(gtfs2emis)
    emi_europe_emep_wear(dist = units::set_units(1,"km"),
                                  speed =  units::set_units(30,"km/h"),
                                  pollutant = c("PM10","TSP","PM2.5"),
                                  veh_type = "Ubus Std 15 - 18 t",
                                  fleet_composition = 1,
                                  load = 0.5,
                                  process = c("tyre"),
                                  as_list = TRUE)
    #> $pollutant
    #> [1] "PM10"  "TSP"   "PM2.5"
    #>
    #> $veh_type
    #> [1] "Ubus Std 15 - 18 t"
    #>
    #> $fleet_composition
    #> [1] 1
    #>
    #> $speed
    #> 30 [km/h]
    #>
    #> $dist
    #> 1 [km]
    #>
    #> $emi
    #>    PM10_tyre_veh_1 TSP_tyre_veh_1 PM2.5_tyre_veh_1
    #>            <units>        <units>          <units>
    #> 1:  0.01873998 [g]  0.0312333 [g]   0.01311799 [g]
    #>
    #> $process
    #> [1] "tyre"

## Brake

The heavy-duty vehicle emission factor is derived by modifying the passenger car emission factor to conform to experimental data obtained from heavy-duty vehicles.

\[EFTSP^{hdv}_{brake} = 1.956 \times LCF_{brake} \times EFTSP^{pc}_{brake}\]

where:

- \(EFTSP^{hdv}_{brake}\) = heavy-duty vehicle emission factor for TSP,
- \(LCF_{brake}\) = load correction factor for brake wear,
- \(EFTSP^{pc}_{brake}\) = passenger car emission factor for TSP.

\[LCF_{brake} = 1 + (0.79 \times LF),\]

where:

- \(LF\) = load factor (-), ranging from 0 for an empty bus to 1 for a fully laden one.

The size distribution of brake wear particles are given by:

particle size class (i) | mass fraction of TSP
--- | ---
TSP | 1.000
PM10 | 0.980
PM2.5 | 0.390
PM1.0 | 0.100
PM0.1 | 0.080

Finally, the speed correction is:

- \(SC_{brake}(speed) = 1.67\), when \(speed < 40 km/h\);
- \(SC_{brake}(speed) = -0.0270 \times speed + 2.75\), when \(40 <= speed <= 95 km/h\);
- \(SC_{brake}(speed) = 0.185\), when \(speed > 95 km/h\).

    emi_europe_emep_wear(dist = units::set_units(1,"km"),
                                  speed =  units::set_units(30,"km/h"),
                                  pollutant = c("PM10","TSP","PM2.5"),
                                  veh_type = "Ubus Std 15 - 18 t",
                                  fleet_composition = 1,
                                  load = 0.5,
                                  process = c("brake"),
                                  as_list = TRUE)
    #> $pollutant
    #> [1] "PM10"  "TSP"   "PM2.5"
    #>
    #> $veh_type
    #> [1] "Ubus Std 15 - 18 t"
    #>
    #> $fleet_composition
    #> [1] 1
    #>
    #> $speed
    #> 30 [km/h]
    #>
    #> $dist
    #> 1 [km]
    #>
    #> $emi
    #>    PM10_brake_veh_1 TSP_brake_veh_1 PM2.5_brake_veh_1
    #>             <units>         <units>           <units>
    #> 1:   0.03349245 [g]  0.03417597 [g]    0.01332863 [g]
    #>
    #> $process
    #> [1] "brake"

## Road Wear

Emissions are calculated according to the equation:

\[TE(i) = dist \times EF^{road}_{tsp}(j) \times mf_{road}\]

where:

- \(TE(i)\) = total emissions of pollutant i (g),
- \(dist\) = total distance driven by vehicles in category j (km),
- \(EF^{road}_{tsp}\) = TSP mass emission factor from road wear for vehicles j (0.0760 g/km),
- \(mf_{road}\) = mass fraction of TSP that can be attributed to particle size class i (-).

The following table shows the size distribution of road surface wear particles

particle size class (i) | mass fraction of TSP
--- | ---
TSP | 1.00
PM10 | 0.50
PM2.5 | 0.27

    emi_europe_emep_wear(dist = units::set_units(1,"km"),
                                  speed =  units::set_units(30,"km/h"),
                                  pollutant = c("PM10","TSP","PM2.5"),
                                  veh_type = "Ubus Std 15 - 18 t",
                                  fleet_composition = 1,
                                  load = 0.5,
                                  process = c("road"),
                                  as_list = TRUE)
    #> $pollutant
    #> [1] "PM10"  "TSP"   "PM2.5"
    #>
    #> $veh_type
    #> [1] "Ubus Std 15 - 18 t"
    #>
    #> $fleet_composition
    #> [1] 1
    #>
    #> $speed
    #> 30 [km/h]
    #>
    #> $dist
    #> 1 [km]
    #>
    #> $emi
    #>    PM10_road_veh_1 TSP_road_veh_1 PM2.5_road_veh_1
    #>            <units>        <units>          <units>
    #> 1:       0.038 [g]      0.076 [g]      0.02052 [g]
    #>
    #> $process
    #> [1] "road"

## Viewing Emissions

Users can also use one single function to apply for more than one process (e.g. tire, brake and road), as shown below.

    library(units)
    library(ggplot2)

    emis_list <- emi_europe_emep_wear(dist = units::set_units(rep(1,100),"km"),
                         speed =  units::set_units(1:100,"km/h"),
                         pollutant = c("PM10","TSP","PM2.5"),
                         veh_type = c("Ubus Std 15 - 18 t"),
                         fleet_composition = c(1),
                         load = 0.5,
                         process = c("brake","tyre","road"),
                         as_list = TRUE)
    ef_dt <- gtfs2emis::emis_to_dt(emis_list,emi_vars = "emi"
                                   ,segment_vars = "speed")
    ggplot(ef_dt)+
      geom_line(aes(x = as.numeric(speed),y = as.numeric(emi),color = pollutant))+
      facet_wrap(facets = vars(process))+
      labs(x = "Speed (km/h)",y = "Emissions (g)")+
      theme_minimal()

When using the `transport_model()` output, users can also visualize both hot-exhaust and non-exhaust emissions taking few more steps. This can be done in three main stages: a) Preparing the data, b) Creating spatial grid; c) Generating spatial and temporal visualizations.

### a) Preparing the data

    library(gtfstools)
    library(sf)

    # read GTFS
    gtfs_file <- system.file("extdata/bra_cur_gtfs.zip", package = "gtfs2emis")
    gtfs <- gtfstools::read_gtfs(gtfs_file)

    # keep a single trip_id to speed up this example
    gtfs_small <- gtfstools::filter_by_trip_id(gtfs, trip_id ="4451136")

    # run transport model
    tp_model <- transport_model(gtfs_data = gtfs_small,
                                spatial_resolution = 100,
                                parallel = FALSE)

    # Fleet data, using Brazilian emission model and fleet
    fleet_data_ef_emep <- data.frame(veh_type = "Ubus Std 15 - 18 t",
                                     fleet_composition = 1,
                                     euro = "V",   # for hot-exhaust emissions
                                     fuel = "D",   # for hot-exhaust emissions
                                     tech = "SCR") # for hot-exhaust emissions
    # Emission model (hot-exhaust)
    emi_list_he <- emission_model(
      tp_model = tp_model,
      ef_model = "ef_europe_emep",
      fleet_data = fleet_data_ef_emep,
      pollutant = "PM10"
    )

    # Emission model (non-exhaust)
    emi_list_ne <- emi_europe_emep_wear(
      dist = tp_model$dist,
      speed = tp_model$speed,
      pollutant = "PM10",
      veh_type = c("Ubus Std 15 - 18 t"),
      fleet_composition = c(1),
      load = 0.5,
      process = c("brake","tyre","road"),
      as_list = TRUE)

    emi_list_ne$tp_model <- tp_model

### b) Creating spatial grid

    # create spatial grid
    grid <- sf::st_make_grid(
      x = sf::st_make_valid(tp_model)
      , cellsize = 0.25 / 200
      , crs= 4326
      , what = "polygons"
      , square = FALSE
    )

    # grid (hot-exhaust)
    emi_grid_he <- emis_grid( emi_list_he,grid,time_resolution = 'day'
                              ,aggregate = TRUE)
    setDT(emi_grid_he)
    pol_names <- setdiff(names(emi_grid_he),"geometry")
    emi_grid_he_dt <- melt(emi_grid_he,measure.vars = pol_names,id.vars = "geometry")
    emi_grid_he_dt <- sf::st_as_sf(emi_grid_he_dt)

    # grid (non-exhaust)
    emi_grid_ne <- emis_grid( emi_list_ne,grid,time_resolution = 'day'
                           ,aggregate = TRUE)
    setDT(emi_grid_ne)
    pol_names <- setdiff(names(emi_grid_ne),"geometry")
    emi_grid_ne_dt <- melt(emi_grid_ne,measure.vars = pol_names,id.vars = "geometry")
    emi_grid_ne_dt <- sf::st_as_sf(emi_grid_ne_dt)

    # bind grid
    emi_grid_dt <- data.table::rbindlist(l = list(emi_grid_he_dt,emi_grid_ne_dt))
    emi_grid_sf  <- sf::st_as_sf(emi_grid_dt)

### c) Generating spatial and temporal patterns

    # plot
    library(ggplot2)

    ggplot(emi_grid_sf) +
      geom_sf(aes(fill= as.numeric(value)), color=NA) +
      geom_sf(data = tp_model$geometry,color = "black")+
      scale_fill_continuous(type = "viridis")+
      labs(fill = "PM10 (g)")+
      facet_wrap(facets = vars(variable),nrow = 1)+
      theme_void()

The total emissions can be also viewed in bar graphics

    # Emissions by time
    emi_time_he <- emis_summary(emi_list_he,by = "time")
    emi_time_ne <- emis_summary(emi_list_ne,by = "time")

    emi_time <- data.table::rbindlist(l = list(emi_time_he,emi_time_ne))

    ggplot(emi_time)+
      geom_col(aes(x = process,y = as.numeric(emi),fill = as.numeric(emi)))+
      scale_fill_continuous(type = "viridis")+
      labs(fill = "PM10 level",y = "Emissions (g)")+
      theme_minimal()

## References

EMEP/EEA data and reports can be accessed in the following links:

- 2019 edition EMEP-EEA.

## Report a bug

If you have any suggestions or want to report an error, please visit the package GitHub page.