rPET - Physiological Equivalent Temperature
The goal of rPET is to calculate and map Physiological Equivalent Temperature (PET) using a 3d point cloud and measurements from sensors in the field and data on the metabolic characteristics of a person. The following input can be used: - air temperature, - wind speed - sun radiation - relative humidity - age - clothing - metabolic rate (standing, walking, running etc..) - weight - height
Mean radiant temperature (Tmrt), a key component of PET, is estimated in this version in a simplified form, i.e. only considering direct and diffuse sunlight, without other surfaces that could be emitting long-wave radiation (i.e. heat).
Mean radiant temperature can be mapped using environmental 3D information. The software can use a terrain model (a raster grid with height of ground) and a 3D point cloud in the form of an XYZ table. These information is used to infer the amount of direct/diffuse solar radiation reaching a person standing at each node of the raster grid, therefore providing Tmrt and the final PET value for that node. For more info see [1-5]:
Usage
Three air temperatures and wind speeds:
library(rPET)
options(digits=3)
PETcorrected( Tair = 20, Tmrt=21, v_air =0, rh=20 )## [1] 21.5
Heavy clothing, cold (5°C) and in shade (no solar radiation)
PETcorrected( Tair = 5, Tmrt=5, v_air=0.1, rh=20, icl = 0 )## [1] 6.12
PETcorrected( Tair = 30, Tmrt=21, v_air=0.5, rh=20 )## [1] 25.1
a faster way in vectorized format, like running each row from table below:
| Tair | Tmrt | v_air | rh |
|---|---|---|---|
| 20 | 30 | 0 | 20 |
| 25 | 30 | 1 | 20 |
| 30 | 30 | 5 | 20 |
PETcorrected( Tair = c(20,25,30), Tmrt=30, v_air=c(0, 1, 5), rh=20 )## [1] 26.8 24.2 26.4
All possible combinations of three values from three factors for a total of 27 combinations.
values <- expand.grid(
Tair = c(20,25,30), Tmrt = 30,
wind_speed = c(0, 1, 5),
rh = c(10, 50, 70)
)
PETcorrected( Tair = values$Tair, Tmrt=values$Tmrt,
v_air=values$wind_speed, rh=values$rh )## [1] 26.7 28.5 30.3 20.4 24.1 28.2 16.8 21.3 26.2 27.2 29.1 31.1 20.7 24.6 29.0
## [16] 16.9 21.6 26.9 27.4 29.4 31.5 20.9 24.8 29.3 17.0 21.7 27.4
Plotting combinations of 10 values from two factors, Air Temperature and Wind Speed:
Tair_values <- (1:20)*2
wind_speed_values <- (1:20)/4
values.dry <- expand.grid(
Tair = Tair_values,
windSpeed = wind_speed_values
)
values.dry$PET <- rPET::PETcorrected( Tair = values.dry$Tair,
Tmrt = values.dry$Tair,
v_air=values.dry$windSpeed,
rh=10 )
topo.loess <- loess (PET ~ Tair * windSpeed, values.dry, degree = 2, span = 0.2)
x <- seq (min (values.dry$Tair), max (values.dry$Tair), .05)
y <- seq (min (values.dry$windSpeed), max (values.dry$windSpeed), .05)
interpolated <- predict (topo.loess, expand.grid (Tair = x, windSpeed = y))
image (x= x, y= y, z = interpolated, xlab = "Air Temp. °C",
ylab="Wind Speed (m/s)", col=hcl.colors(100, "Temps") )
contour(x, y, interpolated, levels = seq(0, 40, by = 2),
add = TRUE, col = "brown", labcex=0.8)
title(main = "Estimated PET values ", font.main = 4)
Mapping confort values
If you have a Digital Terrain Model and a point cloud 3D model as XYZ format format, then you can simulate and map PET over the DTM grid nodes, simulating PET at the position of each node.
NB: what changes is the Mean Radiant Temperature, which is estimated by using 3D data.
## The LAS/LAZ file where the XYZ points are read
# las.file <- "data-raw/voxel_villabolasco_light.laz"
# dtm.file <- "data-raw/bolasco_DTM_1m.tif"
## reading data from the LAS/LAZ file
# xyz<- lidR::readLAS(las.file, select = "XYZ")
## convert LAS data to XYZ table
# PointCloud3D<-xyz@data
## reading DTM
# heightraster <- terra::rast(dtm.file)
## In this example we will use embedded data in the GitHub page
## of the package.
e<-environment(rPET::prepareData)
if(is.null(e$dataenv) ||
!is.data.frame(e$dataenv$pointcloud)||
!inherits(e$dataenv$dtm, "PackedSpatRaster") ){
ret<-rPET::prepareData()
if(!ret) {
warning("Could not download data!")
}
}
## Grab the point cloud from the environment
PointCloud3D<-e$dataenv$pointcloud
heightraster<- terra::unwrap(e$dataenv$dtm)
sunangle = 135 # South East direction of azimuth in degrees
sunaltitude = 45 # 45° from the horizon
##calculate the direct/diffuse fraction using dithered shade
## fraction
rs <- rPET::ray_shade(heightraster,
PointCloud3D,
sunangle = sunangle,
zscale = 1,
sunaltitude = sunaltitude,
makeVoxelGrid = FALSE, progbar = FALSE,
lambert = TRUE)
# rs %>% rayshader::plot_map()
## convert matrix to a terra raster object
rast.shade <- rPET::matrix2raster(rs)
## get non-NA cells' ids
cell.ids <-terra::cells(rast.shade)
## get non-NA cell values
values<- terra::values(rast.shade, na.rm=TRUE)
## to drastically increase speed, we classify
## direct/diffuse fraction in 100 maximum classes
## from 0 to 1 by 0.01 steps
dvalues <- round(values[,1], 2)
udvalues <- unique(dvalues)
## we estimate the mean radiant temperature for the possible
## fraction categories
mrtv <- mrt(air_temperature = 30,
sunaltitude = sunaltitude,
solar_radiation_wm2 = 100,
Fd = udvalues)
## we estimate the PET for the fraction categories
pet.low.wind <- rPET::PETcorrected(Tair = 30, Tmrt =mrtv,
v_air = 0.1, rh = 50 )
## moderate wind 15 km/h -
pet.med.wind <- rPET::PETcorrected(Tair = 30, Tmrt =mrtv,
v_air = 4, rh = 50 )
## we map pet values to all non-NA pixels
all.pet.values.low <- pet.low.wind[ match(dvalues, udvalues) ]
all.pet.values.med <- pet.med.wind[ match(dvalues, udvalues) ]
petraster <- c(heightraster, heightraster)
names(petraster) <- c("low", "med")
## we assign PET values to cells in the heightraster
petraster$low[cell.ids] <- all.pet.values.low
petraster$med[cell.ids] <- all.pet.values.med
range <- quantile(petraster[], c(0.1,0.9), na.rm=TRUE)
# petraster <- terra::clamp(petraster, lower=range[[1]], upper=range[[2]])
terra::plot(petraster, col=viridis::turbo(12),
main=c("PET 0.1 m/s wind", "PET 5 m/s wind") )
title( "30 °C - 50% RH ", cex.main = 1.2, outer=F )Below an animation of mapped comfort index changing over a hot
summer day in Villa Bolasco. 
Solar illumination is simulated at points in space using a 3D model in
voxel structure and a ray-casting method.
gif_file.mp4
**Figure 1.** Example over a UAV lidar flight with 5000 points per square meter.
Installation
Not yet available in CRAN: download and install the development version from GitHub/fpirotti/rPET with:
# install.packages("devtools")
devtools::install_github("fpirotti/rPET")References
-
Pirotti F, Piragnolo M, D’Agostini M, Cavalli R. Information Technologies for Real-Time Mapping of Human Well-Being Indicators in an Urban Historical Garden. Future Internet. 2022; 14(10):280. https://doi.org/10.3390/fi14100280
-
E. Walther, Q. Goestchel, The P.E.T. comfort index: Questioning the model, Building and Environment, Volume 137, 2018, Pages 1-10, ISSN 0360-1323, https://doi.org/10.1016/j.buildenv.2018.03.054.
-
Höppe, P. The physiological equivalent temperature – a universal index for the biometeorological assessment of the thermal environment. Int J Biometeorol 43, 71–75 (1999). https://doi.org/10.1007/s004840050118
-
Rakha, T., Zhandand Christoph Reinhart, P., 2017. A Framework for Outdoor Mean Radiant Temperature Simulation: Towards Spatially Resolved Thermal Comfort Mapping in Urban Spaces. Presented at the 2017 Building Simulation Conference. https://doi.org/10.26868/25222708.2017.677
-
Csilla V. Gál, Noémi Kántor, Modeling mean radiant temperature in outdoor spaces, A comparative numerical
simulation and validation study, Urban Climate, Volume 32, 2020, 100571, https://doi.org/10.1016/j.uclim.2019.100571. -
Morgan-Wall, T., 2023. rayshader: Create Maps and Visualize Data in 2D and 3D. RayShader function for mapping estimated solar radiation values was taken partly from the work of tylermorganwal’s rayshader for R and adapted to point clouds. For more detail on point clouds see Pirotti et al., 2022
Future work
Using a classified point cloud (XYZC) with C=class value to calculate a more sophisticated Tmrt estimation using long-wave radiation emissions from surfaces.
Acknowledgements
This work is part of the VARCITIES project,
that has received funding from the European Union’s Horizon 2020
Research and Innovation programme, under grant agreement No 869505.
This page reflect only the authors’ view and the European
Commission/EASME is not responsible for any use that may be made of the
information it contains.
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