Week_1
Shannon
April 2, 2016
Summary of Combined Land-Surface Air and Sea-Surface Water Temperature Anomalies (Land-Ocean Temperature Index, LOTI)
load("/Users/shannoncall/Desktop/ESCI597A/Week01/climate_Time_Series_Extravaganza.Rdata")
summary(loti.ts)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.77000 -0.22000 -0.05000 0.02167 0.21750 1.35000Plot Dataset
plot(loti.ts)
Figure 1. Land-Surface Air and Sea-Surface Water Temperature index over time
Linear Model
tsp(loti.ts)## [1] 1880.000 2016.083 12.000Histogram of loti data, with a normal curve,
my.xlim <- range(loti.ts)
h<-hist(loti.ts, breaks=10, col="darkorchid4", xlab="Land-Ocean Temperature Index",
main="",xlim=my.xlim)
xfit<-seq(min(loti.ts),max(loti.ts),length=100)
yfit<-dnorm(xfit,mean=mean(loti.ts),sd=sd(loti.ts))
yfit <- yfit*diff(h$mids[1:2])*length(loti.ts)
lines(xfit, yfit, col="darkolivegreen4", lwd=2)
boxplot(loti.ts, horizontal=TRUE, outline=TRUE, axes=FALSE,
ylim=my.xlim, col = "darkorange", add = TRUE, boxwex=3)
Figure 2. Histogram of Land-Ocean Temperature Index
LotiTime <- time(loti.ts)
Loti.lm <- lm(loti.ts ~ LotiTime)
summary(Loti.lm)##
## Call:
## lm(formula = loti.ts ~ LotiTime)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.57565 -0.14028 -0.00237 0.13641 0.85608
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.350e+01 2.351e-01 -57.41 <2e-16 ***
## LotiTime 6.940e-03 1.207e-04 57.51 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1918 on 1632 degrees of freedom
## Multiple R-squared: 0.6696, Adjusted R-squared: 0.6694
## F-statistic: 3307 on 1 and 1632 DF, p-value: < 2.2e-16Add some filters.
I decided to do every 10 and 20 years since that is the interval of years on the graph.
ma20 <- filter(x=loti.ts, filter=rep(x=1/10,times=20), sides=2)
ma10 <- filter(x=loti.ts, filter=rep(x=1/5,times=10), sides=2)Plot those filters
plot(loti.ts,col="dodgerblue4")
lines(ma20,col="firebrick4",lwd=2)
lines(ma10,col="goldenrod3",lwd=2)
abline(Loti.lm, col="darkslateblue",lwd=2, lty="dashed")
Figure 3. Land-Surface Air and Sea-Surface Water Temperature from 1880 - current
f <- frequency(loti.ts)
filt <- c(0.5, rep(1, times=f-1), 0.5)/f
m.hat <- filter(x=loti.ts, filter=filt)
s.hat <- loti.ts - m.hat
par(mfcol=c(2,1))Plot of temperature in Celcius over time
plot(s.hat,ylab="Temperature Celcius")
Figure 4. Temperature in Celcius over time
Boxplot of temperature in Celcius by month
boxplot(s.hat~cycle(s.hat),xlab="Month",ylab="Temperature Celcius")
Figure 5. Boxplot of temperature in Celcius by month
Decomposition
loti.ts.d <- decompose(loti.ts)
plot(loti.ts.d) 
Figure 6. Decomposition of additive time series over time. Looks like the has been increasing since the 1980s. Wonder why… cough fossil fuels cough
New Data: Earthquakes per year from 1900 thru 1998
setwd("/Users/shannoncall/Desktop/ESCI597A/Week01")
read.csv("eqperyear.csv",header=T)## Year Number.of.earthquakes.per.year.magnitude.7.0.or.greater..1900.1998
## 1 1900 13
## 2 1901 14
## 3 1902 8
## 4 1903 10
## 5 1904 16
## 6 1905 26
## 7 1906 32
## 8 1907 27
## 9 1908 18
## 10 1909 32
## 11 1910 36
## 12 1911 24
## 13 1912 22
## 14 1913 23
## 15 1914 22
## 16 1915 18
## 17 1916 25
## 18 1917 21
## 19 1918 21
## 20 1919 14
## 21 1920 8
## 22 1921 11
## 23 1922 14
## 24 1923 23
## 25 1924 18
## 26 1925 17
## 27 1926 19
## 28 1927 20
## 29 1928 22
## 30 1929 19
## 31 1930 13
## 32 1931 26
## 33 1932 13
## 34 1933 14
## 35 1934 22
## 36 1935 24
## 37 1936 21
## 38 1937 22
## 39 1938 26
## 40 1939 21
## 41 1940 23
## 42 1941 24
## 43 1942 27
## 44 1943 41
## 45 1944 31
## 46 1945 27
## 47 1946 35
## 48 1947 26
## 49 1948 28
## 50 1949 36
## 51 1950 39
## 52 1951 21
## 53 1952 17
## 54 1953 22
## 55 1954 17
## 56 1955 19
## 57 1956 15
## 58 1957 34
## 59 1958 10
## 60 1959 15
## 61 1960 22
## 62 1961 18
## 63 1962 15
## 64 1963 20
## 65 1964 15
## 66 1965 22
## 67 1966 19
## 68 1967 16
## 69 1968 30
## 70 1969 27
## 71 1970 29
## 72 1971 23
## 73 1972 20
## 74 1973 16
## 75 1974 21
## 76 1975 21
## 77 1976 25
## 78 1977 16
## 79 1978 18
## 80 1979 15
## 81 1980 18
## 82 1981 14
## 83 1982 10
## 84 1983 15
## 85 1984 8
## 86 1985 15
## 87 1986 6
## 88 1987 11
## 89 1988 8
## 90 1989 7
## 91 1990 13
## 92 1991 10
## 93 1992 23
## 94 1993 16
## 95 1994 15
## 96 1995 25
## 97 1996 22
## 98 1997 20
## 99 1998 16eq<-read.csv("eqperyear.csv",header=T)
numb<-eq$Number.of.earthquakes.per.year.magnitude.7.0.or.greater..1900.1998
earthquakes<-ts(numb,start=c(1900,2),end=c(1998,2),frequency=2)Plot Earthquakes
plot(earthquakes,ylab="Earthquakes per year")
Figure 7. Earthquakes per year, since 1900 thru 1998
my.xlim <- range(earthquakes)
h<-hist(earthquakes, breaks=5, col="deeppink4", xlab="Number of Earthquakes",
main="",xlim=my.xlim)
xfit<-seq(min(earthquakes),max(earthquakes),length=8)
yfit<-dnorm(xfit,mean=mean(earthquakes),sd=sd(earthquakes))
yfit <- yfit*diff(h$mids[1:2])*length(earthquakes)
lines(xfit, yfit, col="darkturquoise", lwd=2)
boxplot(earthquakes, horizontal=TRUE, outline=TRUE, axes=FALSE,
ylim=my.xlim, col = "peachpuff2", add = TRUE, boxwex=3)
Figure 8. Histogram of the number of earthquakes per year.
Now, let’s complete a linear model of our data.
eqtime <- time(earthquakes)
earthquakes.lm <- lm(earthquakes ~ eqtime)
summary(earthquakes.lm)##
## Call:
## lm(formula = earthquakes ~ eqtime)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.189 -5.090 -0.053 3.945 21.504
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 68.27796 35.37817 1.930 0.0551 .
## eqtime -0.02474 0.01815 -1.364 0.1743
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.242 on 195 degrees of freedom
## Multiple R-squared: 0.009446, Adjusted R-squared: 0.004366
## F-statistic: 1.859 on 1 and 195 DF, p-value: 0.1743Looks like there is a downward trend of -0.02474 earthquakes over time. Weird, not sure what that means.
Add Moving Averages and Trend Lines
ma3 <- filter(x=earthquakes, filter=rep(x=1/4,times=4), sides=2)
ma12 <- filter(x=earthquakes, filter=rep(x=1/10,times=10), sides=2)Now let’s plot this thing!
plot(earthquakes,col="steelblue4")
lines(ma3,col="lightsalmon3",lwd=2)
lines(ma12,col="olivedrab3",lwd=2)
abline(earthquakes.lm, col="magenta2",lwd=2, lty="dashed")
Figure 9. Filter with a four and ten year centered moving average.
A trend isn’t very clear. Let’s decompose to see what happens…
Decomposition
earthquakes.d<-decompose(earthquakes)
plot(earthquakes.d)