The rise of sea levels in recent years

Abstract

This exercise is uses data from the archive of the University of Hawaii Sea Level Center to determine the rate of change in the sea level in recent years.

1 Introduction

One of the effects of global warming has been the melting of the polar ice at such a rate that it is contributing to the elevation of sealevels.¹

In this study, we will take historical data of sealevels from 4 locations and determine the annual rise of sealevels in recent years. The data from 4 locations were chosen (i.e., Chittagong,² Halifax,³ Singapore,⁴ and Yap.⁵) and are marked on the map given below.

Loading required package: maps

2 Research Question

3 Methodology

The following datasets were chosen and downloaded from the University of Hawaii Sea Level Center archive.

Datasets included in this study

File ID	CITY, COUNTRY	Description	LATITUDE, LONGITUDE	Dates of record
h124a	Chittagong, Bangladesh	Flood prone area	22.24700, 91.82500	2007-07-01 to 2018-12-06
h275a	Halifax, Canada	Large tidal swells	44.667100, -63.58300	1895-10-16 to 2014-08-12
h327a	Keppel Harbour, Singapore	Busy shallow harbor	1.26300, 103.82200	1981-08-14 to 1990-01-30
h008b	Yap, Micronesia	Shallow open ocean	9.51700, 138.13300	1969-05-11 to 2018-12-31

The data was cleaned, tidied and transformed using the various libraries associated with Tidyverse⁶. The ggplot⁷ package was used to visual the results of analysis of the datasets. The data was prepared and analyzed using the following workflow:

library(tidyverse)

── Attaching packages ──────────────────────────────────────── tidyverse 1.3.1 ──
✓ ggplot2 3.3.5     ✓ purrr   0.3.4
✓ tibble  3.1.3     ✓ dplyr   1.0.7
✓ tidyr   1.1.3     ✓ stringr 1.4.0
✓ readr   2.0.0     ✓ forcats 0.5.1
── Conflicts ─────────────────────────────────────────── tidyverse_conflicts() ──
x dplyr::filter() masks stats::filter()
x dplyr::lag()    masks stats::lag()
x purrr::map()    masks maps::map()

• The CSV versions of the hourly datasets were downloaded for the target locations. The each dataset was loaded into R and trimmed for analysis. The missing data points and unused columns were removed from each of datasets.

loaddata <- function(cnt) {
   fnames =  c("h124a","h275a","h327a","h008b")
   dat = read_csv(paste("datasets/",fnames[cnt],".csv",sep=""),
                  col_names = c("yr","mon","day","hr","level"),
                  col_types = c("i","i","i","i","i"))
   dat = dat %>% 
       filter(level > -1) %>%
       mutate(tm5 = (as.integer(yr / 5) * 5)) %>%
       select(c(yr,tm5,level))
}

• Annual and decade averages were calculated for the data sets. An overall plot of the variation was made. Regression analysis were used to determine the annual rate of change. The annual rate and its standard error were extracted from the regression summary.

extractregression <- function(lm) {
   llm = summary(lm)
   lllm = round(llm$coefficients[2,1:2],4)
} 

• The datasets were reloaded and subjected to linear regression to determine the annual rate of increment.

city = c("Chittagong","Halifax","Singapore","Yap")
sumdat = c("City","StartYr","EndYr","Missing","Existing",
           "Annual Rise","err", "Rise5","err5")
colors = rainbow(4)
plot(-1,-1,xlim=c(0,7500),ylim=c(0,0.001),xlab="Sea levels",ylab="Frequency",
     main="Range of sealevels observed")

for (cnt in c(1:4)) {
   dat = loaddata(cnt)
   l = length(dat$yr)
   d = density(dat$level,bw=20)
   lm = lm(dat$level ~ dat$yr)
   lm5 = lm(dat$level ~ dat$tm5) 
   rate = extractregression(lm)
   rate5 = extractregression(lm5)
   lines(d$x,d$y,lwd=2,col=colors[cnt])
   sumdat = rbind(sumdat,c(city[cnt],
         min(dat$yr),max(dat$yr),
         365*24 * (1+max(dat$yr)-min(dat$yr)) - l,l,
         rate[1], rate[2], rate5[1], rate5[2]))
}

legend(5000,0.0008, city,fill=colors)

3.1 Density plots

The range of sealevels experience within a single year or a 5 yr period were calculated this way.

draw_density <- function(cnt,type) {
fnames =  c("h124a","h275a","h327a","h008b")
city = c("Chittagong","Halifax","Singapore","Yap")
   dat = read_csv(paste("datasets/",fnames[cnt],".csv",sep=""),
                  col_names = c("yr","mon","day","hr","level"),
                  col_types = c("i","i","i","i","i"))
   dat2 = dat %>% 
       filter(level > -1) %>%
       mutate(tm5 = (as.integer(yr / 5) * 5)) %>%
       select(c(yr,tm5,level))
   if (type=="Y") {
      lb = ": comparison of yr to yr"
   dat2 %>%
       ggplot(aes(x=level))+
       geom_density(mapping=aes(x=level,color=yr,group=yr))+
       scale_color_gradient(low="#99000066",high="#FFFF0066")+
       labs(title=paste(city[cnt],lb))
   } else {
      lb = ": comparison of 5yr data units"
   dat2 %>%
       ggplot(aes(x=level))+
       geom_density(mapping=aes(x=level,color=tm5,group=tm5),lwd=2)+
       scale_color_gradient(low="#99000066",high="#FFFF0066")+
       labs(title=paste(city[cnt],lb))
}
}

3.2 Boxplots

Boxplots were also drawn to illustrate the progression of the mean sealevel.

draw_boxplot <- function(cnt,type) {
fnames =  c("h124a","h275a","h327a","h008b")
city = c("Chittagong","Halifax","Singapore","Yap")
   dat = read_csv(paste("datasets/",fnames[cnt],".csv",sep=""),
                  col_names = c("yr","mon","day","hr","level"),
                  col_types = c("i","i","i","i","i"))
   dat2 = dat %>% 
       filter(level > -1) %>%
       mutate(tm5 = (as.integer(yr / 5) * 5)) %>%
       select(c(yr,tm5,level))
   if (type=="Y") {
      lb = ": comparison of yr to yr"
   dat2 %>%
       ggplot(aes(x=yr,y=level,group=yr))+
       geom_boxplot(mapping=aes(x=yr,y=level))+
       labs(title=paste(city[cnt],lb))
   } else {
      lb = ": comparison of 5yr data units"
   dat2 %>%
       ggplot(aes(x=tm5,y=level,group=tm5))+
       geom_boxplot(mapping=aes(x=tm5,y=level))+
       labs(title=paste(city[cnt],lb))
}
}

3.3 Summary of the datasets

knitr::kable(sumdat[,c(1:5)])

sumdat	City	StartYr	EndYr	Missing	Existing
	Chittagong	2007	2018	8402	96718
	Halifax	1895	2014	233879	817321
	Singapore	1981	1990	14309	73291
	Yap	1969	2018	42280	395720

4 Results

Each country has a different story to tell. The analysis of the datasets are displayed in the following table. Summary plots for the range of sealevels experienced over 5 year periods are given for each country in the following sections.

sumdat[1,c(6:9)] = c("Freq:","Yr by yr","Freq:","5yr")
knitr::kable(sumdat[,c(1,6:9)])

		Estimate	Std. Error	Estimate	Std. Error
sumdat	City	Freq:	Yr by yr	Freq:	5yr
	Chittagong	-4.4997	1.3383	-2.4598	1.1955
	Halifax	2.7503	0.0186	2.7555	0.0186
	Singapore	12.0778	1.0691	10.1245	1.0331
	Yap	2.6788	0.0426	2.5486	0.0425

4.1 Year to year comparisons

• Chittagong, Bangladesh

draw_density(1,"Y")

• Halifax, Canada

draw_density(2,"Y")

• Singapore

draw_density(3,"Y")

• Yap, Micronesia

draw_density(4,"Y")

5 Summary

5.1 Chittagong

draw_density(1,"T")

draw_boxplot(1,"Y")

• The sensors are on a buoy in the estuary from a major river flowing from Myanmar.
• Near 60% of Bangladesh’s land mass was flooded (>2m) annually during rainy season.
• The river flooding was severe (>4 m) before the river was dredged.
• Dredging changed the lowtide readings but the high tide readings continued to increase with time.
• The progress being made in dredging and flood prevention (10cm per yr) masks whatever effects increasing sealevel might be (2mm per yr)

5.2 Halifax

draw_density(2,"T")

draw_boxplot(2,"Y")

• Sensors on a buoy at the mouth of the harbor.
• The tidal bay changes the shape of the tidal curve but helps to given constant readings.
• Initially the sealevels were constant but the rise in sealevel has been ongoing for 100 years.

5.3 Singapore

draw_density(3,"T")

draw_boxplot(3,"Y")

• Dredging and widening of the channel contributed to height of the tides.
• Changes in rain patterns and flash flooding of 1980 contributed to a rise the sealevel readings.
• After 1980, the sea levels have a consistent rise.

5.4 Yap

draw_density(4,"T")

draw_boxplot(4,"Y")

• Sensors were located on an offshore buoy where they were not bothered by tidal resistance of the shoreline.
• The tidal levels were far more regular than other harbor readings.
• There seems to a steady increment since 1990, the increase in the size and number of typhoons have had an effect of the sea level measured in recent years..

In short, the tides have been rising approximately 2mm per year around the globe. However, storms, flooding, earthquake driven tsunamis, and even the daily tides create short term local variations that can mask the effects of global sea changes. However, long term studies particularly of offshore buoys clearly illustrate the trend towards higher tides over time. However, data from offshore buoys were often lost particularly in the yearly years of operation.

6 Reference

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1. David Guggenhiem, 2006. An Inconvenient Truth. A documentary film based on Al Gore’s slide presentation. Released by Paramount Films↩︎

2. University of Hawaii Sea Level Center, 2016. Legacy Data Archives: Readings from Chittagong, Bangladesh: http://uhslc.soest.hawaii.edu/data/csv/rqds/indian/hourly/h124a.csv↩︎

3. University of Hawaii Sea Level Center, 2016. Legacy Data Archives: Readings from Halifax, Canada: Downloaded from http://uhslc.soest.hawaii.edu/data/csv/rqds/atlantic/hourly/h275a.csv↩︎

4. University of Hawaii Sea Level Center, 2016. Legacy Data Archives: Readings from Keppel Harbor, Singapore. Downloaded from http://uhslc.soest.hawaii.edu/data/csv/rqds/pacific/hourly/h327a.csv↩︎

5. University of Hawaii Sea Level Center, 2016. Legacy Data Archives: Readings from Yap, Micronesia. Downloaded from http://uhslc.soest.hawaii.edu/data/csv/rqds/pacific/hourly/h008b.csv↩︎

6. Hadly Wickham et al., (2019). Welcome to the tidyverse. Journal of Open Source Software, 4(43), 1686↩︎

7. Hadly Wickham, 2016. ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag, New York.↩︎