wind {Splinets}

Data on wind direction and speed.

Description

NASA/POWER CERES/MERRA2 Native Resolution Hourly Data

• Dates: 01/01/2015 through 03/05/2015

• Location: Latitude 25.7926 Longitude -80.3239

• Elevation from MERRA-2: Average for 0.5 x 0.625 degree lat/lon region = 5.4 meters

Data frame fields:

• YEAR – Year of a measurement

• MO – Month of a measurement

• DY – Day of a measurement

• HR – Hour of a measurement

• WD10M – MERRA-2 Wind Direction at 10 Meters (Degrees)

• WS50M – MERRA-2 Wind Speed at 50 Meters (m/s)

• WD50M – MERRA-2 Wind Direction at 50 Meters (Degrees)

• WS10M – MERRA-2 Wind Speed at 10 Meters (m/s)

Usage

data(wind)

Format

numerical 1536 x 8 dataframe: wind

References

The data was obtained from the National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC) Prediction of Worldwide Energy Resource (POWER) Project funded through the NASA Earth Science/Applied Science Program. https://power.larc.nasa.gov/data-access-viewer/

Examples

#------------------------------------------------#
#----------- Plotting the Wind data -------------#
#------------------------------------------------#

data(wind) #activating the data

wind1=wind[,-1] #Removing YEAR as irrelevant

#Transforming data to daily with the periodic form, i.e. the arguments in [0,1], 
#which is required in the periodic case.

numbdays=length(wind1[,1])/24 

Days=vector(mode='list', length=numbdays)

for(i in 1:numbdays){
  Days[[i]]=wind1[i*(1:24),]
  Days[[i]][,c(4,6)]=Days[[i]][,c(4,6)]/360 #the direction in [0,1]
}

#Raw discretized data for the first day 

par(mfrow=c(2,2))
hist(Days[[1]][,4],xlim=c(0,1),xlab='Wind direction',main='First day 10[m]')
hist(Days[[1]][,6],xlim=c(0,1),xlab='Wind direction',main='First day 50[m]')

plot(Days[[1]][,4],Days[[1]][,5],xlim=c(0,1),pch='.',cex=4,xlab='Wind direction',ylab='Wind speed')
plot(Days[[1]][,6],Days[[1]][,7],xlim=c(0,1),pch='.',cex=4,xlab='Wind direction',ylab='Wind speed')

#First Day Data:
#Projections of the histograms to the periodic spline form 

FirstDayDataF1=cbind(hist(Days[[1]][,4],xlim=c(0,1),breaks=seq(0,1,by=0.1))$mids,
hist(Days[[1]][,4],xlim=c(0,1),breaks=seq(0,1,by=0.1))$counts)


k=3
N=2 
n_knots=2^N*k-1 #the number of internal knots for the dyadic case
xi = seq(0, 1, length.out = n_knots+2) 
#Note that the range of the argument is assumed to be between 0 and 1

PrF1=project(FirstDayDataF1,xi,periodic = TRUE, graph = TRUE)

F1=PrF1$sp #The first day projection of the direction histogram at 10[m]

#Projections of the scatterplots to the periodic spline form 
#The bivariate sampl
FirstDayDataF1V1=as.matrix(Days[[1]][,4:5]) #we note that wind directions are scaled but not ordered 

#Padding the data with zeros as the sampling frequency is not sufficiently dense over [0,1]
FirstDayDataF1V1=rbind(FirstDayDataF1V1,cbind(seq(0,1,by=1/24),rep(0,25)))

#Another knot selection with more knots but still dyadic case
k=4
N=3 
n_knots2=2^N*k-1 #the number of internal knots for the dyadic case
xi2 = seq(0, 1, length.out = n_knots2+2) 

#For illustration one can plot the B-splines and the corresponding splinet
so = splinet(xi2,smorder = k, periodic = TRUE,norm = TRUE) 

plot(so$bs)
plot(so$bs,type='dyadic') #To facilitate the comparison with the splinet better 
                          #one can choose the dyadic grapph
plot(so$os)


#Projecting direction/wind data onto splines
PrS1=project(FirstDayDataF1V1,xi2,smorder=k,periodic = TRUE, graph = TRUE)

S1=PrS1$sp

#the next 7 days 
days= 7
#Transforming to the periodic data 

#The direction histogram
for(i in 2:days){
  DataF1=cbind(hist(Days[[i]][,4],plot=FALSE,breaks=seq(0,1,by=0.1))$mids,
               hist(Days[[i]][,4],plot=FALSE,breaks=seq(0,1,by=0.1))$counts)
  PrF1=project(DataF1,xi,periodic = TRUE)
  
  F1=gather(F1,PrF1$sp) #Collecting projections of daily wind-direction histograms at 10[m]
  
}

plot(F1) #plot of all daily functional data wind direction distributions


#Wind direction vs speed data at 10[m]
for(i in 2:days){
  DataF1V1=as.matrix(Days[[i]][,4:5]) #we note that wind directions are scaled but not ordered 
  
  #Padding the data with zeros as the sampling frequency is not sufficiently dense over [0,1]
  DataF1V1=rbind(DataF1V1,cbind(seq(0,1,by=1/24),rep(0,25)))
  
  PrS1=project(DataF1V1,xi2,smorder=k,periodic = TRUE)
  
  S1=gather(S1,PrS1$sp) #Collecting projections of daily wind-direction histograms at 10[m]
  
}

plot(S1) #plot of all daily functional data wind speed at wind direction

#Computing means of the data
A=matrix(rep(1/days,days),ncol=days)

MeanF1=lincomb(F1,A)
plot(MeanF1)

MeanS1=lincomb(S1,A)
plot(MeanS1)