Venice Maximum Sea Levels Data
Some sea levels data sets recorded at Venice, Italy.
data(venice) data(venice90)
venice is a data frame with 51 observations on the following 11
variables.
It concerns the maximum heights of sea levels between
1931 and 1981.
a numeric vector.
numeric vectors;
r1 is the highest recorded value,
r2 is the second highest recorded value, etc.
venice90 is a data frame with 455 observations on the following
7 variables.
numeric vectors; actual time of the recording.
numeric; sea level.
numeric; number of hours since the midnight of 31 Dec 1939 and 1 Jan 1940.
numeric vector;
approximate year as a real number.
The formula is start.year + ohour / (365.26 * 24)
where start.year is 1940.
One can treat Year as continuous whereas
year can be treated as both continuous and discrete.
Sea levels are in cm.
For venice90, the value 0 corresponds to a fixed
reference point (e.g., the mean sea level in 1897 at an old
palace of Venice). Clearly since the relative (perceived)
mean sea level has been increasing in trend over time (more
than an overall 0.4 m increase by 2010), therefore the value 0 is
(now) a very low and unusual measurement.
For venice, in 1935 only the top six values were recorded.
For venice90, this is a subset of a data set provided by
Paolo Pirazzoli consisting of hourly sea levels from 1940 to 2009.
Values greater than 90 cm were extracted, and then declustered
(each cluster provides no more than one value, and
each value is at least 24 hours apart).
Thus the values are more likely to be independent.
Of the original (2009-1940+1)*365.26*24 values
about 7 percent of these comprise venice90.
Yet to do: check for consistency between the data sets. Some external data sets elsewhere have some extremes recorded at times not exactly on the hour.
Pirazzoli, P. (1982) Maree estreme a Venezia (periodo 1872–1981). Acqua Aria, 10, 1023–1039.
Thanks to Paolo Pirazzoli and Alberto Tomasin for the venice90
data.
Smith, R. L. (1986). Extreme value theory based on the r largest annual events. Journal of Hydrology, 86, 27–43.
Battistin, D. and Canestrelli, P. (2006). La serie storica delle maree a Venezia, 1872–2004 (in Italian), Comune di Venezia. Istituzione Centro Previsione e Segnalazioni Maree.
## Not run:
matplot(venice[["year"]], venice[, -1], xlab = "Year",
ylab = "Sea level (cm)", type = "l")
ymat <- as.matrix(venice[, paste("r", 1:10, sep = "")])
fit1 <- vgam(ymat ~ s(year, df = 3), gumbel(R = 365, mpv = TRUE),
data = venice, trace = TRUE, na.action = na.pass)
head(fitted(fit1))
par(mfrow = c(2, 1), xpd = TRUE)
plot(fit1, se = TRUE, lcol = "blue", llwd = 2, slty = "dashed")
par(mfrow = c(1,1), bty = "l", xpd = TRUE, las = 1)
qtplot(fit1, mpv = TRUE, lcol = c(1, 2, 5), tcol = c(1, 2, 5),
llwd = 2, pcol = "blue", tadj = 0.1)
plot(sealevel ~ Year, data = venice90, type = "h", col = "blue")
summary(venice90)
dim(venice90)
round(100 * nrow(venice90) / ((2009 - 1940 + 1) * 365.26 * 24), digits = 3)
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