Regional scale model
The model at regional scale is the same as running the model at “punctual” scale for each cell of the grid but without accounting for active or passive dispersal. Each cell is therefore a close unit or mosquito population. With this setting, the model requires two input datasets:
- a numerical temperature matrix (in degree Celsius) defined in space and time (space in the rows, time in the columns);
- a two-column numerical matrix reporting the centroid coordinates (in meters) of each cell.
For the purpose of this tutorial, we will use the following simulated datasets:
- A 5 km lattice grid with 250 m cell size;
- A 1-year long spatially and temporally correlated temperature time series;
Prepare input data
Create lattice arena
First, we define the physical space into which the introduction of our mosquitoes will happen. We define a squared lattice arena having 5 km side and 250 m resolution (20 colums and 20 rows, 400 total cells).
gridDim <- 20 # 5000m/250 m = 20 columns and rows
xy <- expand.grid(x=1:gridDim, y=1:gridDim)We then add a spatial pattern into the lattice area. This spatial pattern will be used later to add spatial correllation (SAC) to the temperature time series. The spatial autocorrelated pattern will be obtained using a semivariogram model with defined sill (value that the semivarion attains at the range) and range (distance of 0 spatial correlation) and then predicting the semivariogram model over the lattice grid using unconditional Gaussian simulation.
varioMod <- vgm(psill=0.5, range=100, model='Exp') # psill = partial sill = (sill-nugget)
# Set up an additional variable from simple kriging
zDummy <- gstat(formula=z~1,
locations = ~x+y,
dummy=TRUE,
beta=1,
model=varioMod,
nmax=1)
# Generate a randomly autocorrelated predictor data field
set.seed(123)
xyz <- predict(zDummy, newdata=xy, nsim=1)# [using unconditional Gaussian simulation]We generate a spatially autocorrelated raster adding the SA variable (xyz$sim1) to the RasterLayer object. The autocorrelated surface could for example represent the distribution of vegetation cover in a urban landscape.
utm32N <- "+proj=utm +zone=32 +ellps=WGS84 +datum=WGS84 +units=m +no_defs"
r <- raster(nrow=gridDim, ncol=gridDim, crs=utm32N, ext=extent(1220000,1225000, 5700000,5705000))
values(r)=xyz$sim1
plot(r)
df <- data.frame("id"=1:nrow(xyz), raster::coordinates(r))
bbox <- as(extent(r), "SpatialPolygons")
# Store Parameters for autocorrelation
autocorr_factor <- values(r)Simulate temperature data with seasonal trend
We first simulate a 1-year temperature time series with seasonal trend. For the time series we consider a mean value of 16°C and standard deviation of 2°C.
ndays = 365*1 #length of the time series in days
set.seed(123)
sim_temp <- create_sims(n_reps = 1,
n = ndays,
central = 16,
sd = 2,
exposure_type = "continuous",
exposure_trend = "cos1", exposure_amp = -1.0,
average_outcome = 12,
outcome_trend = "cos1",
outcome_amp = 0.8,
rr = 1.0055)A visualisation of the distribution of temperature values and temporal trend.
hist(sim_temp[[1]]$x,
xlab="Temperature (°C)",
main="Histogram of simulated temperatures")
plot(sim_temp[[1]]$date,
sim_temp[[1]]$x,
main="Simulated temperatures seasonal trend",
xlab="Date", ylab="Temperature (°C)"
)
We can then “expand onto space” the temperature time series by multiplying it with the autocorrelated surface simulated above.
mat <- lapply(1:ncell(r), function(x) {
d_t <- sim_temp[[1]]$x*autocorr_factor[[x]]
return(d_t)
})
mat <- do.call(rbind,mat)oldpar <- par(mfrow = c(1,2)) A comparison between the distribution of the initial temperature time series and autocorrelated temperature surface
par(mfrow=c(2,1))
hist(mat, xlab="Temperature (°C)", main="Histogram of simulated spatial autocorreled temperatures")
hist(sim_temp[[1]]$x, xlab="Temperature (°C)", main="Histogram of simulated temperatures", col="red")
par(mfrow=c(1,1))par(oldpar) 
