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FourStep_Algorithm.R
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#Table S1 R-code for calculating the four-Step algorithm
rm(list = ls())
if (! require (gamlss)) {install.packages ("gamlss")}
if (! require (gamlss.dist)) {install.packages ("gamlss.dist")}
library(gamlss)
library(gamlss.dist)
#setwd("C:/mydocuments/") #setting the work directory
data.matrix=read.csv("mydata.csv", header=TRUE,sep=",")
#maydata.csv is 3-column a csv file (the input file).
#1st column is the years;
#2nd is the months (1 to 12)
#3rd is the monthly rainfall amounts
#For example
#Years Month Rain
#1900 1 150
#[...] [...] [...]
#2020 12 200
mumber.time.scales=12 # Must range between 1 and 12
n.locals=length(data.matrix[1,])-2
for (ts in 1:mumber.time.scales){
time.scale=ts
suitable.dist.deltaAICc=matrix(NA,12,n.locals)
N=length(data.matrix[,1])
moderate=matrix(NA,12,n.locals)
severe=matrix(NA,12,n.locals)
extreme=matrix(NA,12,n.locals)
for (local in 1:n.locals){
rain=as.matrix(data.matrix[,(local+2)])
colnames(rain)=c("rain")
year=data.matrix[,1]
month=data.matrix[,2]
data.orig=as.data.frame(cbind(year,month,rain))
nt=length(data.orig$month)
data=matrix(NA,(nt-12),3)
rain=matrix(NA,nt,1)
for (end in time.scale:(nt)){
rain[end,1]=(sum(data.orig$rain[(end-(time.scale-1)):end]))}
data=na.omit(as.data.frame(cbind(data.orig$year, data.orig$month,
rain)))
colnames(data)=c("year","month","rain")
data=data[order(data$month),]
for (month in 1:12){
i.month=which(data$month==month)
data.by.month=as.matrix(na.omit(data[min(i.month):max(i.month),]))
n=length(data.by.month[,1])
time=as.matrix(seq(1:n))
x.axis=as.matrix(qnorm(ppoints(n)))
SPI.gamma=matrix(NA,n,1)
probacum.gamma=matrix(NA,n,1)
non.rain.data.boolean=data.by.month[,3]>0
id=which(data.by.month[,3]>0)
time.nonzero=as.matrix(time[id])
non.rain.data=as.matrix(data.by.month[,3][non.rain.data.boolean])
np=length(non.rain.data); nz=n-np; data.by.month[,3][data.by.month[,
3]<0]=0
probzero=(nz+1)/(2*(n+1))
t.gam=gamlss(non.rain.data~1,family=GA, mu.link = "identity",
sigma.link ="log")
t.gam.ns10=gamlss(non.rain.data~poly(time.nonzero,1),family=GA,
mu.link = "identity", sigma.link ="log")
t.gam.ns11=gamlss(non.rain.data~poly(time.nonzero,1), sigma.formula
=~poly(time.nonzero,1), family=GA, mu.link = "identity", sigma.link ="log")
probacum.gamma=as.matrix(probzero+(1-probzero)*pGA(data.by.month[,3],
mu = t.gam$mu.fv[1], sigma = t.gam$sigma.fv[1], lower.tail = TRUE, log.p =
FALSE))
for (t in 1:n){
if (probacum.gamma[t,1]<=0.5){sinal=sqrt(log(1/probacum.gamma[t,
1]^2))
SPI.gamma[t,1]=-1*(sinal-
(2.515517+0.802853*sinal+0.010328*sinal^2)/
(1+1.432788*sinal+0.189269*sinal^2+0.001308*sinal^3))}
else{sinal=sqrt(log(1/(1-probacum.gamma[t,1])^2))
SPI.gamma[t,1]=sinal-(2.515517+0.802853*sinal+0.010328*sinal^2)/
(1+1.432788*sinal+0.189269*sinal^2+0.001308*sinal^3)}
}
AICc.gamma=AIC(t.gam, k=2, c=TRUE)
AICc.nsgamma10=AIC(t.gam.ns10, k=2, c=TRUE)
AICc.nsgamma11=AIC(t.gam.ns11, k=2, c=TRUE)
akaikec=cbind(AICc.gamma,AICc.nsgamma10,AICc.nsgamma11)
delta.akaikec=as.data.frame(akaikec-akaikec[which.min(akaikec)])
best.dist.AICc=delta.akaikec[which(delta.akaikec==0)]
suitable.dist.AICc=colnames(best.dist.AICc)
LRT=(1-pchisq(-(t.gam.ns10$P.deviance-t.gam$P.deviance),1))
if (LRT>0.05){suitable.dist.LRT="model1"}else{
LRT=(1-pchisq(-(t.gam.ns11$P.deviance-t.gam.ns10$P.deviance),1))
if(LRT>0.05){suitable.dist.LRT="model2"}
else{suitable.dist.LRT="model3"}}
delta.test.AICc=which(delta.akaikec<=2)
if (length(delta.test.AICc)==3)
{suitable.dist.deltaAICc[month,local]=suitable.dist.LRT}
if (length(delta.test.AICc)==1){
if (suitable.dist.AICc=="AICc.gamma")
{suitable.dist.deltaAICc[month,local]="model1"}
if (suitable.dist.AICc=="AICc.nsgamma10")
{suitable.dist.deltaAICc[month,local]="model2"}
if (suitable.dist.AICc=="AICc.nsgamma11")
{suitable.dist.deltaAICc[month,local]="model3"}}
if (length(delta.test.AICc)==2){
if (delta.test.AICc[1]==1 && delta.test.AICc[2]==2){
if (t.gam.ns10$G.deviance<t.gam$G.deviance){
LRT=LR.test(t.gam,t.gam.ns11, print="FALSE")
if (LRT$p.val>=0.05){suitable.dist.deltaAICc[month,local]="model1"}
else{suitable.dist.deltaAICc[month,local]="model2"}}
else{suitable.dist.deltaAICc[month,local]="model1"}}
if (delta.test.AICc[1]==1 && delta.test.AICc[2]==3){
if (t.gam.ns11$G.deviance<t.gam$G.deviance){
LRT=LR.test(t.gam,t.gam.ns11, print="FALSE")
if (LRT$p.val>=0.05)
{suitable.dist.deltaAICc[month,local]="model1"}
else{suitable.dist.deltaAICc[month,local]="model3"}}
else{suitable.dist.deltaAICc[month,local]="model1"}}
if (delta.test.AICc[1]==2 && delta.test.AICc[2]==3){
if (t.gam.ns11$G.deviance<t.gam.ns10$G.deviance){
LRT=LR.test(t.gam.ns10,t.gam.ns11, print="FALSE")
if (LRT$p.val>=0.05)
{suitable.dist.deltaAICc[month,local]="model2"}
else{suitable.dist.deltaAICc[month,local]="model3"}}
else{suitable.dist.deltaAICc[month,local]="model2"}}}
p.moderate.drought=(pnorm(-1, mean=0, sd=1))
p.severe.drought=(pnorm(-1.5, mean=0, sd=1))
p.extreme.drought=(pnorm(-2, mean=0, sd=1))
p.chuva.moderate=(p.moderate.drought-probzero)/(1-probzero)
p.chuva.severe=(p.severe.drought-probzero)/(1-probzero)
p.chuva.extreme=(p.extreme.drought-probzero)/(1-probzero)
if(p.chuva.moderate>0){
moderate.rain=qGA(p.chuva.moderate,mu = t.gam$mu.fv[1], sigma =
(t.gam$sigma.fv[1]),lower.tail = TRUE, log.p = FALSE)}
else{moderate.rain=0}
if(p.chuva.severe>0){
severe.rain=qGA(p.chuva.severe,mu = t.gam$mu.fv[1], sigma =
t.gam$sigma.fv[1],lower.tail = TRUE, log.p = FALSE)}
else{severe.rain=0}
if(p.chuva.extreme>0){
extreme.rain=qGA(p.chuva.extreme,mu = t.gam$mu.fv[1], sigma =
t.gam$sigma.fv[1],lower.tail = TRUE, log.p = FALSE)}
else{extreme.rain=0}
if (suitable.dist.deltaAICc[month,local]=="model1"){
actual.prob.moderate=100*pnorm(-1, mean=0, sd=1, lower.tail=TRUE)
actual.prob.severe=100*pnorm(-1.5, mean=0, sd=1, lower.tail=TRUE)
actual.prob.extreme=100*pnorm(-2, mean=0, sd=1, lower.tail=TRUE)
mu.trend=0; sigma.trend=0
}
if (suitable.dist.deltaAICc[month,local]=="model2"){
f=length(t.gam.ns10$mu.fv)
timevarying.moderate=as.matrix(pGA(moderate.rain, mu =
t.gam.ns10$mu.fv, sigma = t.gam.ns10$sigma.fv, lower.tail = TRUE, log.p =
FALSE))
timevarying.severe=as.matrix(pGA(severe.rain, mu =
t.gam.ns10$mu.fv, sigma = t.gam.ns10$sigma.fv, lower.tail = TRUE, log.p =
FALSE))
timevarying.extreme=as.matrix(pGA(extreme.rain, mu =
t.gam.ns10$mu.fv, sigma = t.gam.ns10$sigma.fv, lower.tail = TRUE, log.p =
FALSE))
mu.trend=t.gam.ns10$mu.coefficients[2]; sigma.trend=0
actual.prob.moderate=100*(probzero+(1-
probzero)*(timevarying.moderate[f]))
actual.prob.severe=100*(probzero+(1-
probzero)*(timevarying.severe[f]))
actual.prob.extreme=100*(probzero+(1-
probzero)*(timevarying.extreme[f]))
}
if (suitable.dist.deltaAICc[month,local]=="model3"){
f=length(t.gam.ns10$mu.fv)
timevarying.moderate=as.matrix(pGA(moderate.rain, mu =
t.gam.ns11$mu.fv, sigma = t.gam.ns11$sigma.fv, lower.tail = TRUE, log.p =
FALSE))
timevarying.severe=as.matrix(pGA(severe.rain, mu =
t.gam.ns11$mu.fv, sigma = t.gam.ns11$sigma.fv, lower.tail = TRUE, log.p =
FALSE))
timevarying.extreme=as.matrix(pGA(extreme.rain, mu =
t.gam.ns11$mu.fv, sigma = t.gam.ns11$sigma.fv, lower.tail = TRUE, log.p =
FALSE))
mu.trend=t.gam.ns11$mu.coefficients[2];
sigma.trend=t.gam.ns11$sigma.coefficients[2]
actual.prob.moderate=100*(probzero+(1-
probzero)*(timevarying.moderate[f]))
actual.prob.severe=100*(probzero+(1-
probzero)*(timevarying.severe[f]))
actual.prob.extreme=100*(probzero+(1-
probzero)*(timevarying.extreme[f]))
}
if(p.moderate.drought>probzero){
moderate[month,local]=actual.prob.moderate}
else{moderate[month,local]="too many zeros"}
if(p.severe.drought>probzero){
severe[month,local]=actual.prob.severe}
else{severe[month,local]="too many zeros"}
if(p.extreme.drought>probzero){
extreme[month,local]=actual.prob.extreme}
else{extreme[month,local]="too many zeros"}
}}
colnames(moderate)=c("Moderate")
colnames(severe)=c("Severe")
colnames(extreme)=c("Extreme")
if (ts==1){finalts1=format(cbind(moderate,severe,extreme),digits = 2)}
if (ts==2){finalts2=format(cbind(moderate,severe,extreme),digits = 2)}
if (ts==3){finalts3=format(cbind(moderate,severe,extreme),digits = 2)}
if (ts==4){finalts4=format(cbind(moderate,severe,extreme),digits = 2)}
if (ts==5){finalts5=format(cbind(moderate,severe,extreme),digits = 2)}
if (ts==6){finalts6=format(cbind(moderate,severe,extreme),digits = 2)}
if (ts==7){finalts7=format(cbind(moderate,severe,extreme),digits = 2)}
if (ts==8){finalts8=format(cbind(moderate,severe,extreme),digits = 2)}
if (ts==9){finalts9=format(cbind(moderate,severe,extreme),digits = 2)}
if (ts==10){finalts10=format(cbind(moderate,severe,extreme),digits = 2)}
if (ts==11){finalts11=format(cbind(moderate,severe,extreme),digits = 2)}
if (ts==12){finalts12=format(cbind(moderate,severe,extreme),digits = 2)}
}
final=as.matrix(cbind(finalts1,finalts2,
finalts3,finalts4,finalts5,finalts6,
finalts7,finalts8,finalts9,
finalts10,finalts11,finalts12))
row.names(final)=c("Jan","Feb","Mar","Apr","May","Jun",
"Jul","Ago","Sep","Oct","Nov","Dec")
name.ts=c("","Time Scale 1","",
"","Time Scale 2","",
"","Time Scale 3","",
"","Time Scale 4","",
"","Time Scale 5","",
"","Time Scale 6","",
"","Time Scale 7","",
"","Time Scale 8","",
"","Time Scale 9","",
"","Time Scale 10","",
"","Time Scale 11","",
"","Time Scale 12","")
final=rbind(name.ts,final)
write.csv(final,"Currently_Expected_Frequency.csv")