Timescales for detecting SLR acceleration

Recent interest in a paper on sea level rise acceleration (Haigh et al. 2014) has led me to attempt to reproduce their analysis.

Below is R code that I wrote to examine one of the stations from the paper (Key West). In future posts I will expand on this code to check the “sliding” window portion of the paper.

kw_haigh

  ##obtain annual mean sea level for Key West from:
  #http://www.psmsl.org/data/obtaining/rlr.annual.data/188.rlrdata
  
  dt<-read.table("http://www.psmsl.org/data/obtaining/rlr.annual.data/188.rlrdata",sep=";",header=FALSE,na.strings="-99999")
  names(dt)<-c("date","level")
  dt<-dt[3:97,] #restrict date range to same as reference 1915-2009
  dt[39,2]<-(dt[38,2]+dt[40,2])/2 #fill missing value at 1953 by linear interpolation
  dt[,2]<-dt[,2]-min(dt[,2])#center series

  linearfit<-lm(dt$level~dt$date)
  dt$detrend<-dt$level-(linearfit$coefficients[2]*dt$date)      
  ar1fit<-arima(dt$detrend,order=c(1,0,0)) #fit ar1
  lm(dt$level~poly(dt$date,2,raw=T))$coefficients[3]*2 #check acceleration estimate from table 2
  
  #create ar5 mid projection of 0.5 m (500 mm) incease from 1990 to 2100
  x<-seq(from=0,to=109,by=1)
  y<-x^2*8.25+x*169.25+dt[95,2]#smooth quadratric not from IPCC
  a<-(500-76)/y[length(y)]#scaling factor
  y2<-y[20:110]*a+76
  level2<-append(dt$level-dt[76,2],y2)#down-shift time series to match haigh (level is 0 at 1990)
  level2<-cbind(data.frame(seq(from=1915,to=2100,by=1)),data.frame(level2))
  names(level2)<-c("year","level")
  plot(level2$year,level2$level,type="l",main="Key West",ylab="Level(mm)",xlab="Year",lwd=2)
  
  #simulate future oscillations from ar1fit
  for(i in 1:1000){
  ar.sim<-arima.sim(list(ar=c(as.numeric(ar1fit$coef[1]))),n=length(y2),sd=23)#sd value from haigh et al not able to reproduce
  lines(seq(from=2010,to=2100,by=1),y2+ar.sim,col="grey")
  }
  lines(seq(from=2010,to=2100,by=1),y2+ar.sim,lwd=2)

###Reference

I. D. Haigh, T. Wahl, E. J. Rohling, R. M. Price, C. B. Pattiaratchi, F. M. Calafat, S.Dangendorf, “Timescales for detecting a significant acceleration in sea level rise”, Nature Communications 5, Article number: 3635, http://dx.doi.org/10.1038/ncomms4635, published 14 April 2014.