geosptdb (version 1.0-1)

idwST: Inverse Distance Weighting (IDW) function for spatio-temporal prediction.

Description

This function performs spatio-temporal interpolation. Here idwST is in a local neighborhood. This interpolation method considers the value of a point can be obtained from the weighted sum of values of the regionalized variable of closest neighbors. The general formula for the IDW is given by: $$ \hat{z}_0(st)=\sum_{i=1}^n \lambda_i z_i(st) $$ The expression for determining the weights is: $$ \lambda_i = \frac{d_{i0}^{-p}}{\sum_{i=1}^n d_{i0}^{-p}} $$ The weight is controlled by a factor p with each increment of the distance, \(d_{i0}\) is the distance between the prediction position and each of the measured positions.

The expression \(d_{i0}\) can be obtained by: $$ d_{i0}=\sqrt{(x_{i}-x_{0})^2+(y_{i}-y_{0})^2+C\cdot (t_{i}-t_{0})^2} $$ \(x\), \(y\) and \(t\) correspond to the spatio-temporal coordinates, p (factor.p) and C factors defined below.

Usage

idwST(formula, data, newdata, n.neigh, C, factor.p, progress)

Arguments

formula

formula that defines a detrended linear model, use \(z_{st}\)~1.

data

SpatialPointsDataFrame: should contain the spatio-temporal dependent variable, independent variables (statics and/or dynamics), spatial coordinates and the time as an integer or numerical variable.

newdata

data frame or spatial object with prediction/simulation spatio-temporal locations; should contain attribute columns with the independent variables (if present) and (if locations is a formula) the coordinates and time with names, as defined in locations where you want to generate new predictions

n.neigh

number of nearest observations that should be used for a idwST prediction, where nearest is defined in terms of the spatio-temporal locations

C

numeric; associated to time factor, we recommend using the parameter found by minimizing the root-mean-square prediction errors using cross-validation. Using idwST.cv and optimize

factor.p

numeric; specify the inverse distance weighting power (p is the exponent that influences the weighting or optimal smoothing parameter)

progress

whether a progress bar shall be printed for spatio-temporal inverse-distance weighted function; default=TRUE

Value

Attributes columns contain coordinates, time, predictions, and the variance column contains NA's

Details

idwST function generates individual spatio-temporal predictions from IDW spatio-temporal interpolation. IDW is a type of deterministic method for interpolation, the assigned values to unknown points are calculated with a weighted average of the values available at the known points.

References

Li L, Losser T, Yorke C, Piltner R. (2014). Fast inverse distance weighting-based spatiotemporal interpolation: a web-based application of interpolating daily fine particulate matter PM2:5 in the contiguous U.S. using parallel programming and k-d tree. Int. J. Environ. Res. Public Health, 11: 9101-9141. [link]

Examples

# NOT RUN {
# Loading Croatia data
data(croatia2008)
coordinates(croatia2008) <- ~x+y

# prediction case: one point
point <- data.frame(670863,5043464,5)
names(point) <- c("x","y","t")

coordinates(point) <- ~x+y
idwST(MTEMP~1, data=croatia2008, newdata=point, n.neigh=60, C=1, factor.p=2)

# }
# NOT RUN {
# prediction case: a grid of points Croatia (year 2008)
data(croatia)
points <- spsample(croatia, n=5000, type="regular")

data(croatia2008)
coordinates(croatia2008)<-~x+y

GridsT <- vector(mode = "list", length = 12)

for(i in 1:12){
GridsT[[i]] <- data.frame(points@coords,i)
names(GridsT[[i]]) <- c("x","y","t")
}

idw.croatia <- data.frame(matrix(NA, ncol = 14, nrow=nrow(GridsT[[1]])))
pb <- txtProgressBar(min = 0, max = 12, char = "=", style = 3)
for(i in 1:12){
coordinates(GridsT[[i]]) <- c("x", "y")
idw.croatia[,i+2] <- idwST(MTEMP~1, croatia2008, newdata=GridsT[[i]], n.neigh=10, C=1,
                          factor.p=2, progress=FALSE)[,4]
setTxtProgressBar(pb, i)
}
close(pb)

idw.croatia[,1:2] <- GridsT[[1]]@coords
nam <- paste(c("ENE","FEB","MAR","ABR","MAY","JUN","JUL","AGO","SEP","OCT","NOV","DIC"),
             2008,sep="")
names(idw.croatia) <- c("x","y",nam)

coordinates(idw.croatia) <- c("x", "y")
gridded(idw.croatia) <- TRUE

# show prediction map
pal2 <- colorRampPalette(c("blue3", "wheat1", "red3"))

p1 <- spplot(idw.croatia[,1:12], cuts=30, col.regions=pal2(35), colorkey=F,
            scales = list(draw =T,cex=0.6, abbreviate=TRUE,minlength=1), pch=0.3,
            cex.lab=0.3, cex.title=0.3, auto.key = F, main = "Earth's average
            temperature IDW map 2008", key.space=list(space="right", cex=0.8))

split.screen( rbind(c(0, 1,0,1), c(1,1,0,1)))
split.screen(c(1,2), screen=1)-> ind
screen( ind[1])
p1
screen( ind[2])
image.plot(legend.only=TRUE, legend.width=0.5, col=pal2(100),
           smallplot=c(0.7,0.75, 0.3,0.7), zlim=c(min(idw.croatia@data),
           max(idw.croatia@data)), axis.args = list(cex.axis = 0.7))
close.screen( all=TRUE)
# }