GY667 Assignment 2

The three climate indices that were looked at in this assignment were the El Nino/Southern Oscillation, the Pacific Decadal Oscillation and the ALantic Multidecadal OScillation. The indices were downloaded from this link http://climexp.knmi.nl/selectindex.cgi?id=ididsomeone@somewhere

Using these indices the aim of this assignment is to calculate the correlation patterns and the regression patterns for both Sea Surface Temprature and Sea level Pressure.

The Library

these were the following packages used for the assignment.

library(sp)
library(raster) 
library(ncdf4)
library(rgdal)

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##  Path to PROJ.4 shared files: C:/Users/Kennf/Documents/R/win-library/3.5/rgdal/proj
##  Linking to sp version: 1.3-1

library(RColorBrewer)

## Warning: package 'RColorBrewer' was built under R version 3.5.2

library(lattice)
library(latticeExtra)
library(reshape2)
library(maps)

graphics.off()
rm(list=ls())

The work directory was seet as the following.

setwd("/Users/Kennf/Downloads/GY667workshop3")

The file path was set up as the following.

path <- file.path(getwd(),"data")

Due to complications within the 3rd workshop, the spatial dataframe was loaded directly into R. This was done so to map the data.

load("C:/Users/Kennf/Downloads/GY667workshop3/world.coast.Rdata")

Hadley Sea Surface Temperature.

Before getting the SST and SLP of the three indices so the can be corrlated, the SST and SLP data has to be loaded and calculated.

The SST data was loaded looking at the lat, lon, sst and date.

nc <- nc_open(file.path(getwd(),"HadISST_sst.nc"))
lat <- ncvar_get(nc,"latitude") 
lon <- ncvar_get(nc,"longitude")
sst <- ncvar_get(nc,"sst")
date <- ncvar_get(nc,"time")

The date format was converted.

tunits <- ncatt_get(nc,"time",attname="units")
tustr <- strsplit(tunits$value, " ")
date <- as.character(as.Date(date,origin=unlist(tustr)[3]))

This function replaces missing values with NA. As many datasets have different fill values.

fillvalue <- ncatt_get(nc,"sst","_FillValue")
sst[sst==fillvalue$value] <- NA
missvalue <- ncatt_get(nc,"sst","missing_value")
sst[sst==missvalue$value] <- NA
sst[sst==-1000] <- NA

using the colmeans and rowmeans with the aggregate function was used so that the global mean must be examined.The RColourBrewer was used to add a colour pallete to observe the mapped data.

year <- format(as.Date(date, format="%Y-%m-%d"),"%Y")
gmean <- colMeans(sst, na.rm = TRUE, dims=2)
annmean <- aggregate(gmean,by=list(year),FUN=mean,na.rm=TRUE)
avsst = rowMeans(sst,na.rm=FALSE,dims=2)

colors <- rev(brewer.pal(10, "RdYlBu"))
pal <- colorRampPalette(colors)

The data was plotted used by using the levelplot function.

grid <- expand.grid(x=lon, y=lat)
grid$avsst <- as.vector(avsst)
levelplot(avsst~x*y,grid,col.regions = pal(100),
          xlab='Longitude',ylab='Latitude',main='Average SST'
) + 
  layer(sp.lines(world.coast))

To look at the annual averages, a loop was used that contained the annuak SST data calculated from the monthly data.

yrs <- annmean$Group.1
nyr <- length(yrs)    

asst <- array(NA,c(dim(lon),dim(lat),nyr))
for (k in 1:nyr) {
  asst[,,k] <- rowMeans(sst[,,year==yrs[k]],na.rm=FALSE,dims=2)
}

This was then plotted.

grid$an_avsst <- as.vector(rowMeans(asst,na.rm=FALSE,dims=2))

levelplot(an_avsst~x*y, data=grid,col.regions = pal(100),xlab='Longitude',ylab='Latitude',main='Annually Averaged SST') +
  layer(sp.lines(world.coast)) 

Sea Level Pressure

slp_nc   <- nc_open(file.path(getwd(),"slp.mon.mean.nc"))
slp_lat <- ncvar_get(slp_nc,"lat") 
slp_lon <- ncvar_get(slp_nc,"lon")
slp <- ncvar_get(slp_nc,"slp")
slp_lon <- ifelse(slp_lon<=180,slp_lon,slp_lon-360) ##This code convert the values to work with the longitude data so it can agree with the spatial dataframe.

The SLP data for time used the same code with the expection that the data had to be converted into days rather than hours.

slp_date <-ncvar_get(slp_nc,"time")
tunits<-ncatt_get(slp_nc,"time",attname="units")
tustr<-strsplit(tunits$value, " ")
slp_date <- (slp_date)/24 
slp_date<-as.character(as.Date(slp_date,origin=unlist(tustr)[3]))

fillvalue <- ncatt_get(slp_nc,"slp","_FillValue")
slp[slp==fillvalue$value] <- NA
missvalue <- ncatt_get(slp_nc,"slp","missing_value")
slp[slp==missvalue$value] <- NA
slp[slp==-1000] <- NA

slp_year <- format(as.Date(slp_date, format="%Y-%m-%d"),"%Y")
slp_gmean <- colMeans(slp, na.rm = TRUE, dims=2)
slp_mean <- aggregate(slp_gmean,by=list(slp_year),FUN=mean,na.rm=TRUE)
avslp = rowMeans(slp,na.rm=FALSE,dims=2)

grid2 <- expand.grid(x=slp_lon, y=slp_lat)
grid2$avslp <- as.vector(avslp)
levelplot(avslp~x*y,grid2,col.regions = pal(100),
          xlab='Longitude',ylab='Latitude',main='Average SLP'
) + 
  layer(sp.lines(world.coast))

slp_yrs <- slp_mean$Group.1 
slp_nyr <- length(slp_yrs)

aslp <- array(NA,c(dim(slp_lon),dim(slp_lat),slp_nyr))
for (k in 1:slp_nyr) {
  aslp[,,k] <- rowMeans(slp[,,slp_year==slp_yrs[k]],na.rm=FALSE,dims=2) 
}

grid2$an_avslp <- as.vector(rowMeans(aslp,na.rm=FALSE,dims=2))

levelplot(an_avslp~x*y, data=grid2,col.regions = pal(100),xlab='Longitude',ylab='Latitude',main='Annually Averaged SLP') +
  layer(sp.lines(world.coast))

Climate indices

EL Nino/Southern Oscillation indices.

The data was loaded.

enso_nc <- nc_open("ihadisst1_nino12a.nc")

enso_time <- ncvar_get(enso_nc, "time")
ensounits <- ncatt_get(enso_nc,"time",attname="units")
ensoustr <- strsplit(ensounits$value, " ")
enso_time <- as.character(as.Date(enso_time*365.25/12,origin=unlist(ensoustr)[3])) #this made the file sorted into months as opposed to days.

enso <- ncvar_get(enso_nc, 'Nino12')

fillvalue <- ncatt_get(enso_nc,"Nino12","_FillValue")
enso[enso==fillvalue$value] <- NA
missvalue <- ncatt_get(enso_nc,"Nino12","missing_value")
enso[enso==missvalue$value] <- NA
enso[enso==-1000] <- NA

enso_year <- format(as.Date(enso_time, format="%Y-%m-%d"),"%Y") 
enso_mean <- aggregate(enso,by=list(enso_year),FUN=mean,na.rm=TRUE)

enso_yrs <- enso_mean$Group.1
enso_ts <- enso_mean$x

plot(enso_yrs,enso_ts,type="l",xlab="Year",ylab="Annual ENSO")

The data needed to be overlaaped for the enso and for the sst for the plot to work.

enso_ts <- enso_mean$x[1:148]
asst3 <- asst

Correlation

The corelation is calculated by using a loop which is then added to the dataset.

c.matrix <- matrix(NA,length(lon),length(lat))
t.matrix <- matrix(NA,length(lon),length(lat))

for (i in 1:dim(lon)) {
  for (j in 1:dim(lat)) {
    if (length(asst3[i,j,][!is.na(asst3[i,j,])])>2){
      c.matrix[i,j] <- cor(asst3[i,j,], enso_ts)
      p.vals <- cor.test(asst3[i,j,], enso_ts)
      t.matrix[i, j] <- p.vals$p.value
    }
  }
}

grid$corr <- as.vector(c.matrix)
grid$pval <- as.vector(t.matrix)

Assuming a 99% significance level, subset the grid data where pval.nao < 0.01. The subset is then converted to the data frame for plotting with correlation.

sig <- subset(grid[, c(1, 2, 5, 6)], pval < 0.01)
sig <- SpatialPointsDataFrame(coords = sig[, c(1, 2)], data = sig)

The corrleation is then plotted

levelplot(corr~x*y, data=grid, 
          col.regions = pal(100),xlab='Longitude',ylab='Latitude', main="Correlation of SST with ENSO indice") + 
  layer(sp.lines(world.coast)) +
  layer(sp.points(sig, pch = 20, cex = 0.001, col = "black"))

Regression

r.matrix <- matrix(NA,length(lon),length(lat))
s.matrix <- matrix(NA,length(lon),length(lat))

for (i in 1:dim(lon)) {
  for (j in 1:dim(lat)) {
    if (length(asst3[i,j,][!is.na(asst3[i,j,])])>2){
      r.lm <- lm(asst3[i,j,]~enso_ts)
      r.matrix[i,j] <- r.lm$coefficients[2]
      smm<-summary(r.lm)
      s.matrix[i, j] <- smm$coefficients[8]
    }
  }
}

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## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

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## unreliable

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## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

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## unreliable

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## unreliable

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## unreliable

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## unreliable

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## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

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## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

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## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
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## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

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## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

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## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

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## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
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grid$reg <- as.vector(r.matrix)
grid$sig <- as.vector(s.matrix)

sig <- subset(grid[, c(1, 2, 5, 6)], pval < 0.01)
sig <- SpatialPointsDataFrame(coords = sig[, c(1, 2)], data = sig)

levelplot(reg~x*y, data=grid,   at=c(-10:15)/10,
          col.regions = pal(100),xlab='Longitude',ylab='Latitude',main="Linear Regression of SST with ENSO") + 
  layer(sp.lines(world.coast)) +
  layer(sp.points(sig, pch = 20, cex = 0.001, col = "black"))

Sea level pressure:

Correlation

enso_yrs <- enso_mean$Group.1
enso_ts <- enso_mean$x

The time series is plotted

plot(enso_yrs,enso_ts,type="l",xlab="Year",ylab="Annual ENSO")

To the following was done to get the time to overlap. As the ENSO data goes from 1870 to 2017 where as the SLP data 1948-2018.

enso_ts <- enso_mean$x[79:149]

Correlation between ENSO and SLP data.

c.matrix <- matrix(NA,length(slp_lon),length(slp_lat))
t.matrix <- matrix(NA,length(slp_lon),length(slp_lat))

for (i in 1:dim(slp_lon)) {
  for (j in 1:dim(slp_lat)) {
    if (length(aslp[i,j,][!is.na(aslp[i,j,])])>2){
      c.matrix[i,j] <- cor(aslp[i,j,], enso_ts)
      p.vals <- cor.test(aslp[i,j,], enso_ts)
      t.matrix[i, j] <- p.vals$p.value
    }
  }
}

grid2$corr <- as.vector(c.matrix)
grid2$pval <- as.vector(t.matrix)

sig <- subset(grid2[, c(1, 2, 5, 6)], pval < 0.01)
sig <- SpatialPointsDataFrame(coords = sig[, c(1, 2)], data = sig)

levelplot(corr~x*y, data=grid2, 
          col.regions = pal(100),xlab='Longitude',ylab='Latitude', main="Correlation of SLP with ENSO") + 
  layer(sp.lines(world.coast)) +
  layer(sp.points(sig, pch = 20, cex = 0.001, col = "black"))

r.matrix <- matrix(NA,length(slp_lon),length(slp_lat))
s.matrix <- matrix(NA,length(slp_lon),length(slp_lat))

for (i in 1:dim(slp_lon)) {
  for (j in 1:dim(slp_lat)) {
    if (length(aslp[i,j,][!is.na(aslp[i,j,])])>2){
      r.lm <- lm(aslp[i,j,]~enso_ts)
      r.matrix[i,j] <- r.lm$coefficients[2]
      smm<-summary(r.lm)
      s.matrix[i, j] <- smm$coefficients[8]
    }
  }
}

grid2$reg <- as.vector(r.matrix)
grid2$sig <- as.vector(s.matrix)

sig <- subset(grid2[, c(1, 2, 5, 6)], pval < 0.01)
sig <- SpatialPointsDataFrame(coords = sig[, c(1, 2)], data = sig)

levelplot(reg~x*y, data=grid2,   at=c(-23:20)/10,
          col.regions = pal(100),xlab='Longitude',ylab='Latitude',main="Linear Regression of SLP with ENSO") + 
  layer(sp.lines(world.coast)) +
  layer(sp.points(sig, pch = 20, cex = 0.001, col = "black"))

The ENSO has a strongest positive correlation within the Pacific. Whereas the strongest negative correlation in the Atlantic Ocean.

SSTs within the period of 2000 to 2010 is believed to be a result of a higher frequency of the ENSO cycle. However longer data sets would be able to understand how exactly the ENSO effects the SST of the globe (McPhaden, 2012).

Pacific Decadal Oscilliation

pdo_nc <- nc_open("ipdo_hadsst3.nc")

pdo_time <- ncvar_get(pdo_nc, "time")
pdounits <- ncatt_get(pdo_nc,"time",attname="units")
pdoustr <- strsplit(pdounits$value, " ")
pdo_time <- as.character(as.Date(pdo_time*365.25/12,origin=unlist(pdoustr)[3]))

pdo <- ncvar_get(pdo_nc, 'index')

fillvalue <- ncatt_get(pdo_nc,"index","_FillValue")
pdo[pdo==fillvalue$value] <- NA
missvalue <- ncatt_get(pdo_nc,"index","missing_value")
pdo[pdo==missvalue$value] <- NA
pdo[pdo==-1000] <- NA

pdo_year <- format(as.Date(pdo_time, format="%Y-%m-%d"),"%Y") 
pdo_mean <- aggregate(pdo,by=list(pdo_year),FUN=mean,na.rm=TRUE)

pdo_yrs <- pdo_mean$Group.1
pdo_ts <- pdo_mean$x

plot(pdo_yrs,pdo_ts,type="l",xlab="Year",ylab="Annual PDO", main="Annual PDO")

For the PDO time series ranged from 1899 to 2019 where as the sst time series ranged from 1870 to 2017.

pdo_ts <- pdo_mean$x[16:134]
asst2 <- asst[,,30:148]  

c.matrix <- matrix(NA,length(lon),length(lat))
t.matrix <- matrix(NA,length(lon),length(lat))

for (i in 1:dim(lon)) {
  for (j in 1:dim(lat)) {
    if (length(asst2[i,j,][!is.na(asst2[i,j,])])>2){
      c.matrix[i,j] <- cor(asst2[i,j,], pdo_ts)
      p.vals <- cor.test(asst2[i,j,], pdo_ts)
      t.matrix[i, j] <- p.vals$p.value
    }
  }
}

grid$corr <- as.vector(c.matrix)
grid$pval <- as.vector(t.matrix)

sig <- subset(grid[, c(1, 2, 5, 6)], pval < 0.01)
sig <- SpatialPointsDataFrame(coords = sig[, c(1, 2)], data = sig)

levelplot(corr~x*y, data=grid, 
          col.regions = pal(100),xlab='Longitude',ylab='Latitude', main="Correlation of SST with PDO") + 
  layer(sp.lines(world.coast)) +
  layer(sp.points(sig, pch = 20, cex = 0.001, col = "black"))

Regression

r.matrix <- matrix(NA,length(lon),length(lat))
s.matrix <- matrix(NA,length(lon),length(lat))

for (i in 1:dim(lon)) {
  for (j in 1:dim(lat)) {
    if (length(asst2[i,j,][!is.na(asst2[i,j,])])>2){
      r.lm <- lm(asst2[i,j,]~pdo_ts)
      r.matrix[i,j] <- r.lm$coefficients[2]
      smm<-summary(r.lm)
      s.matrix[i, j] <- smm$coefficients[8]
    }
  }
}

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## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
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## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

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## unreliable

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## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

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## unreliable

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## unreliable

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## unreliable

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## unreliable

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## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

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## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

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## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
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## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

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## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

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## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

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## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

## Warning in summary.lm(r.lm): essentially perfect fit: summary may be
## unreliable

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grid$reg <- as.vector(r.matrix)
grid$sig <- as.vector(s.matrix)

sig <- subset(grid[, c(1, 2, 5, 6)], pval < 0.01)
sig <- SpatialPointsDataFrame(coords = sig[, c(1, 2)], data = sig)

levelplot(reg~x*y, data=grid,   at=c(-8:8)/10,
          col.regions = pal(100),xlab='Longitude',ylab='Latitude',main="Linear Regression of SST with PDO") + 
  layer(sp.lines(world.coast)) +
  layer(sp.points(sig, pch = 20, cex = 0.001, col = "black"))

Sea level pressure

pdo_yrs <- pdo_mean$Group.1
pdo_ts <- pdo_mean$x

plot(pdo_yrs,pdo_ts,type="l",xlab="Year",ylab="Annual PDO")

pdo_ts <- pdo_mean$x[65:135]
aslp2 <- aslp  

c.matrix <- matrix(NA,length(slp_lon),length(slp_lat))
t.matrix <- matrix(NA,length(slp_lon),length(slp_lat))

for (i in 1:dim(slp_lon)) {
  for (j in 1:dim(slp_lat)) {
    if (length(aslp2[i,j,][!is.na(aslp2[i,j,])])>2){
      c.matrix[i,j] <- cor(aslp2[i,j,], pdo_ts)
      p.vals <- cor.test(aslp2[i,j,], pdo_ts)
      t.matrix[i, j] <- p.vals$p.value
    }
  }
}

grid2$corr <- as.vector(c.matrix)
grid2$pval <- as.vector(t.matrix)

sig <- subset(grid2[, c(1, 2, 5, 6)], pval < 0.01)
sig <- SpatialPointsDataFrame(coords = sig[, c(1, 2)], data = sig)

levelplot(corr~x*y, data=grid2, 
          col.regions = pal(100),xlab='Longitude',ylab='Latitude', main="Correlation of SLP with PDO") + 
  layer(sp.lines(world.coast)) +
  layer(sp.points(sig, pch = 20, cex = 0.001, col = "black"))

r.matrix <- matrix(NA,length(slp_lon),length(slp_lat))
s.matrix <- matrix(NA,length(slp_lon),length(slp_lat))

for (i in 1:dim(slp_lon)) {
  for (j in 1:dim(slp_lat)) {
    if (length(aslp2[i,j,][!is.na(aslp2[i,j,])])>2){
      r.lm <- lm(aslp2[i,j,]~pdo_ts)
      r.matrix[i,j] <- r.lm$coefficients[2]
      smm<-summary(r.lm)
      s.matrix[i, j] <- smm$coefficients[8]
    }
  }
}

grid2$reg <- as.vector(r.matrix)
grid2$sig <- as.vector(s.matrix)

sig <- subset(grid2[, c(1, 2, 5, 6)], pval < 0.01)
sig <- SpatialPointsDataFrame(coords = sig[, c(1, 2)], data = sig)

levelplot(reg~x*y, data=grid2,   at=c(-24:13)/10,
          col.regions = pal(100),xlab='Longitude',ylab='Latitude',main="Linear Regression of SLP with PDO") + 
  layer(sp.lines(world.coast)) +
  layer(sp.points(sig, pch = 20, cex = 0.001, col = "black"))

Correlation between the PDO indice and the SSt variations orginates within the tropics and is most present within the paccfic. There is a lot of uncertaintiy with how the PDO fully operates. Due to this it’s hard to understand on whether or not the PDO is going through a cool phase, as it varys and changes every 20-30 years (R. Hare and J. Mantua, 2002).

Within the Eastern Pacfic Ocean that is the strongest postive effect and a negative effect within the easter pacfic ocean and the north alantic ocean.

The PDO is has a strong postive effect within the Central ALantic, Indian and African Oceans. There is a strong negative effect on SLP in the Antartic.

ALantic Multidecadal Oscillation

amo_nc <- nc_open("iamo_hadsst_ts.nc")

amo_time <- ncvar_get(amo_nc, "time")
amounits <- ncatt_get(amo_nc,"time",attname="units")
amoustr <- strsplit(amounits$value, " ")
amo_time <- as.character(as.Date(amo_time*365.25/12,origin=unlist(amoustr)[3]))

amo <- ncvar_get(amo_nc, 'AMO')
fillvalue <- ncatt_get(amo_nc,"AMO","_FillValue")
amo[amo==fillvalue$value] <- NA
missvalue <- ncatt_get(amo_nc,"AMO","missing_value")
amo[amo==missvalue$value] <- NA
amo[amo==-1000] <- NA

amo_year <- format(as.Date(amo_time, format="%Y-%m-%d"),"%Y")
amo_mean <- aggregate(amo,by=list(amo_year),FUN=mean,na.rm=TRUE)

amo_yrs <- amo_mean$Group.1 
amo_ts <- amo_mean$x    

plot(amo_yrs,amo_ts,type="l",xlab="Year",ylab="Annual AMO",main="Annual AMO")

amo_ts <- amo_mean$x[26:164]
asst1 <- asst[,,10:148]

Correlation

c.matrix <- matrix(NA,length(lon),length(lat))
t.matrix <- matrix(NA,length(lon),length(lat))

for (i in 1:dim(lon)) {
  for (j in 1:dim(lat)) {
    if (length(asst1[i,j,][!is.na(asst1[i,j,])])>2){
      c.matrix[i,j] <- cor(asst1[i,j,], amo_ts)
      p.vals <- cor.test(asst1[i,j,], amo_ts)
      t.matrix[i, j] <- p.vals$p.value
    }
  }
}

grid$corr <- as.vector(c.matrix)
grid$pval <- as.vector(t.matrix)

sig <- subset(grid[, c(1, 2, 5, 6)], pval < 0.01)
sig <- SpatialPointsDataFrame(coords = sig[, c(1, 2)], data = sig)

Regression

r.matrix <- matrix(NA,length(lon),length(lat))
s.matrix <- matrix(NA,length(lon),length(lat))

for (i in 1:dim(lon)) {
  for (j in 1:dim(lat)) {
    if (length(asst1[i,j,][!is.na(asst1[i,j,])])>2){
      r.lm <- lm(asst1[i,j,]~amo_ts)
      r.matrix[i,j] <- r.lm$coefficients[2]
      smm<-summary(r.lm)
      s.matrix[i, j] <- smm$coefficients[8]
    }
  }
}

grid$reg <- as.vector(r.matrix)
grid$sig <- as.vector(s.matrix)

sig <- subset(grid[, c(1, 2, 5, 6)], pval < 0.01)
sig <- SpatialPointsDataFrame(coords = sig[, c(1, 2)], data = sig)

levelplot(reg~x*y, data=grid , at=c(-16:37)/10,
          col.regions = pal(150),xlab='Longitude',ylab='Latitude',main="Linear Regression of SST with AMO") + 
  layer(sp.lines(world.coast)) +
  layer(sp.points(sig, pch = 20, cex = 0.001, col = "black"))

Sea level pressure

amo_yrs <- amo_mean$Group.1
amo_ts <- amo_mean$x

plot(amo_yrs,amo_ts,type="l",xlab="Year",ylab="Annual AMO")

amo_ts <- amo_mean$x[95:165]
aslp1 <- aslp 

Correlation

c.matrix <- matrix(NA,length(slp_lon),length(slp_lat))
t.matrix <- matrix(NA,length(slp_lon),length(slp_lat))

for (i in 1:dim(slp_lon)) {
  for (j in 1:dim(slp_lat)) {
    if (length(aslp1[i,j,][!is.na(aslp1[i,j,])])>2){
      c.matrix[i,j] <- cor(aslp1[i,j,], amo_ts)
      p.vals <- cor.test(aslp1[i,j,], amo_ts)
      t.matrix[i, j] <- p.vals$p.value
    }
  }
}

grid2$corr <- as.vector(c.matrix)
grid2$pval <- as.vector(t.matrix) 

sig <- subset(grid2[, c(1, 2, 5, 6)], pval < 0.01)
sig <- SpatialPointsDataFrame(coords = sig[, c(1, 2)], data = sig)

levelplot(corr~x*y, data=grid2 , 
          col.regions = pal(100),xlab='Longitude',ylab='Latitude', main="Correlation of SLP with AMO") + 
  layer(sp.lines(world.coast)) +
  layer(sp.points(sig, pch = 20, cex = 0.001, col = "black"))

r.matrix <- matrix(NA,length(slp_lon),length(slp_lat))
s.matrix <- matrix(NA,length(slp_lon),length(slp_lat))

for (i in 1:dim(slp_lon)) {
  for (j in 1:dim(slp_lat)) {
    if (length(aslp1[i,j,][!is.na(aslp1[i,j,])])>2){
      r.lm <- lm(aslp1[i,j,]~amo_ts)
      r.matrix[i,j] <- r.lm$coefficients[2]
      smm<-summary(r.lm)
      s.matrix[i, j] <- smm$coefficients[8]
    }
  }
}

grid2$reg <- as.vector(r.matrix) 
grid2$sig <- as.vector(s.matrix)

sig <- subset(grid2[, c(1, 2, 5, 6)], pval < 0.01)
sig <- SpatialPointsDataFrame(coords = sig[, c(1, 2)], data = sig)

levelplot(reg~x*y, data=grid2 , at=c(-90:101)/10,
          col.regions = pal(200),xlab='Longitude',ylab='Latitude',main="Linear Regression of SLP with AMO") + 
  layer(sp.lines(world.coast)) +
  layer(sp.points(sig, pch = 20, cex = 0.001, col = "black"))

Within the North Alantic the AMO has the strongest impact on the SST, however there is little effect on any of the other oceans other than the North ALantic (Green, Marshall and Donohoe, 2017).

Biblography:

Green, B., Marshall, J. and Donohoe, A. (2017). Twentieth century correlations between extratropical SST variability and ITCZ shifts. Geophysical Research Letters, 44(17), pp.9039-9047.

McPhaden, M. (2012). A 21st century shift in the relationship between ENSO SST and warm water volume anomalies. Geophysical Research Letters, 39(9), p.n/a-n/a.

R. Hare, S. and J. Mantua, J. (2002). Pacific Decadal Oscillation. Journal of Oceanography, 58, pp.35-44.