| Title: | Improved Techniques to Estimate Trend, Velocity and Acceleration from Sea Level Records |
|---|---|
| Description: | Analysis of annual average ocean water level time series from long (minimum length 80 years) individual records, providing improved estimates of trend (mean sea level) and associated real-time velocities and accelerations. Improved trend estimates are based on Singular Spectrum Analysis methods. Various gap-filling options are included to accommodate incomplete time series records. The package also contains a forecasting module to consider the implication of user defined quantum of sea level rise between the end of the available historical record and the year 2100. A wide range of screen and pdf plotting options are available in the package. |
| Authors: | Phil J Watson <[email protected]> |
| Maintainer: | Phil J Watson <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 1.0 |
| Built: | 2024-12-21 06:48:07 UTC |
| Source: | CRAN |
Annual average ocean water level data from Permanent Service for Mean Sea Level (UK).
data(Balt)data(Balt)
Time series data file with the first column the year and the second column the corresponding annual average ocean water level (mm). File contains 112 records spanning the period from 1904 to 2014 with a single missing value in 1990.
The raw (*.csv) form of this data set is used extensively in the examples throughout this manual.
Permanent Service for Mean Sea Level (2015)
Holgate, S.J., Matthews, A., Woodworth, P.L., Rickards, L.J., Tamisiea, M.E., Bradshaw, E., Foden, P.R., Gordon, K.M., Jevrejeva, S. and Pugh, J., 2013. New data systems and products at the Permanent Service for Mean Sea Level. Journal of Coastal Research, 29(3), pp. 493-504.
msl.trend, msl.forecast,
msl.plot, msl.pdf, summary.
data(Balt) plot(Balt, type = "l", xlab = "Year", ylab = "Annual Average Mean Sea Level (mm)", main = 'BALTIMORE, USA') str(Balt) # check structure of data filedata(Balt) plot(Balt, type = "l", xlab = "Year", ylab = "Annual Average Mean Sea Level (mm)", main = 'BALTIMORE, USA') str(Balt) # check structure of data file
Projected sea level rise integrated with historical record.
msl.forecast(object, slr = 800, plot = TRUE)msl.forecast(object, slr = 800, plot = TRUE)
object |
|
slr |
numeric, enables a user defined amount of projected sea level rise in millimetres. The user range is [200 to 1500] where 800 is the default setting. |
plot |
logical, if ‘TRUE’ then the original time series is plotted to the screen along with the trend component, the result of gap filling (where necessary) and the added quantum of sea level rise selected. 95% confidence intervals have also been applied. Default = TRUE. |
This routine adds a user specified quantum of sea level rise
from the end of the deconstructed historical record to the year 2100.
All internal parameters captured in the msl.trend object
are passed directly to msl.forecast.
An object of class “msl.forecast” is returned with the following elements:
the name of the data record.
a summary data frame of relevant attributes relating to the trend and the inputted annual average data set extended to 2100 with projected sea level rise, including:
$Year: input data;
$MSL: input data;
$Trend: mean sea level trend;
$TrendSD: standard deviation of the determined mean sea level trend;
$Vel: velocity (or first derivative) of mean sea level trend (mm/year);
$VelSD: standard deviation of the velocity of the mean sea level trend;
$Acc: acceleration (or second derivative) of mean sea level trend (mm/year/year);
$AccSD: standard deviation of the acceleration of the mean sea level trend; and
$FilledTS: gap-filled time series (where necessary).
outputs the peak velocity and the year in which it occurs.
outputs the peak acceleration and the year in which it occurs.
outputs details of the start, end and length of the input data set.
outputs the extent of missing data (years) in the original record and the gap filling method used (where necessary).
details the amount of sea level rise applied between the end of the historical record and the year 2100.
outputs the number of iterations used to generate the respective standard deviations for error margins.
msl.trend, msl.plot, msl.pdf,
summary, Balt, s, t.
# ------------------------------------------------------------------------- # Isolate trend from Baltimore record, filling gaps with spline interpolation, # 500 iterations and adding 1000 mm of slr to 2100. Use raw 'Balt.csv' data file. # Note: ordinarily user would call 'File.csv' direct from working directory # using the following sample code: # s <- msl.trend('Balt.csv', fillgaps = 3, iter = 500, 'BALTIMORE, USA') # t <- msl.forecast(s, slr = 1000) # ------------------------------------------------------------------------- data(s) # msl.trend object from above-mentioned example data(t) # msl.forecast object from above-mentioned example str(t) # check structure of msl.forecast object msl.plot(s, type=2) # check screen output of gapfilling and trend estimate msl.plot(t, type=2) # check screen output of adding 1000 mm of sea level rise# ------------------------------------------------------------------------- # Isolate trend from Baltimore record, filling gaps with spline interpolation, # 500 iterations and adding 1000 mm of slr to 2100. Use raw 'Balt.csv' data file. # Note: ordinarily user would call 'File.csv' direct from working directory # using the following sample code: # s <- msl.trend('Balt.csv', fillgaps = 3, iter = 500, 'BALTIMORE, USA') # t <- msl.forecast(s, slr = 1000) # ------------------------------------------------------------------------- data(s) # msl.trend object from above-mentioned example data(t) # msl.forecast object from above-mentioned example str(t) # check structure of msl.forecast object msl.plot(s, type=2) # check screen output of gapfilling and trend estimate msl.plot(t, type=2) # check screen output of adding 1000 mm of sea level rise
Pdf plotting options.
msl.pdf(x, file_name = " ", type = 1, ci = 1)msl.pdf(x, file_name = " ", type = 1, ci = 1)
x |
object of class “msl.trend” (see |
file_name |
is a character string indicating the name of the pdf output file. If this field is left blank the output file will be automatically saved in the working directory under the default name "File1.pdf". |
type |
numeric, enables a user defined input to select the type of chart to be plotted. The default setting (type = 1) provides 3 charts in the same plot area with the time series in the top panel, instantaneous velocity in the middle panel and instantaneous acceleration in the bottom panel. The alternatives (2, 3 and 4) are single panel plots of time series, instantaneous velocity and instantaneous acceleration, respectively. |
ci |
numeric, enables a user defined input to select the type of confidence interval to be displayed on the plots. The default setting (ci = 1) corresponds to a 95% confidence interval whilst ci=2 provides a 99% confidence interval. |
This routine provides a range of pdf plotting options for both
“msl.trend” (see msl.trend) and “msl.forecast”
(see msl.forecast) objects. Three panel plots (type 1 or
default) are formatted with width = 16.54 inches and height = 20 inches.
Single panel plots (types 2, 3, 4) are formatted with width = 16.54 inches
and height = 15 inches. All plots are designed to be proportionally correct
when imported into documents and re-sized to the width of a standard A4 page.
The same range of alternative screen plotting options are available via
msl.plot.
msl.trend, msl.forecast,
msl.plot, Balt, s, t.
# ------------------------------------------------------------------------- # Isolate trend from Baltimore record, filling gaps with spline interpolation, # 500 iterations and adding 1000 mm of slr to 2100. Use raw 'Balt.csv' data file. # Note: ordinarily user would call 'File.csv' direct from working directory # using the following sample code: # s <- msl.trend('Balt.csv', fillgaps = 3, iter = 500, 'BALTIMORE, USA') # t <- msl.forecast(s, slr = 1000) # ------------------------------------------------------------------------- data(s) # msl.trend object from above-mentioned example data(t) # msl.forecast object from above-mentioned example # default output, 3 panels, 95% confidence intervals. msl.pdf(s) # Check 'File1.pdf' in working directory # pdf plot time series, 95% confidence intervals. msl.pdf(s, file_name = 'Series.pdf', type = 2) # Check 'Series.pdf' file in working directory # pdf plot instantaneous velocity, 95% confidence intervals. msl.pdf(s, file_name = 'Velocity.pdf', type = 3) # Check 'Velocity.pdf' file in working directory # pdf plot instantaneous acceleration, 99% confidence intervals. msl.pdf(s, file_name = 'Acceleration.pdf', type = 4, ci = 2) # Check 'Acceleration.pdf' file in working directory # default output, 3 panels, 95% confidence intervals. msl.pdf(t, file_name = 'Forecast.pdf') # Check 'Forecast.pdf' file in working directory# ------------------------------------------------------------------------- # Isolate trend from Baltimore record, filling gaps with spline interpolation, # 500 iterations and adding 1000 mm of slr to 2100. Use raw 'Balt.csv' data file. # Note: ordinarily user would call 'File.csv' direct from working directory # using the following sample code: # s <- msl.trend('Balt.csv', fillgaps = 3, iter = 500, 'BALTIMORE, USA') # t <- msl.forecast(s, slr = 1000) # ------------------------------------------------------------------------- data(s) # msl.trend object from above-mentioned example data(t) # msl.forecast object from above-mentioned example # default output, 3 panels, 95% confidence intervals. msl.pdf(s) # Check 'File1.pdf' in working directory # pdf plot time series, 95% confidence intervals. msl.pdf(s, file_name = 'Series.pdf', type = 2) # Check 'Series.pdf' file in working directory # pdf plot instantaneous velocity, 95% confidence intervals. msl.pdf(s, file_name = 'Velocity.pdf', type = 3) # Check 'Velocity.pdf' file in working directory # pdf plot instantaneous acceleration, 99% confidence intervals. msl.pdf(s, file_name = 'Acceleration.pdf', type = 4, ci = 2) # Check 'Acceleration.pdf' file in working directory # default output, 3 panels, 95% confidence intervals. msl.pdf(t, file_name = 'Forecast.pdf') # Check 'Forecast.pdf' file in working directory
Screen plotting options.
msl.plot(x, type = 1, ci = 1)msl.plot(x, type = 1, ci = 1)
x |
object of class “msl.trend” (see |
type |
numeric, enables a user defined input to select the type of chart to be plotted. The default setting (type = 1) provides 3 charts in the same plot area with the time series in the top panel, instantaneous velocity in the middle panel and instantaneous acceleration in the bottom panel. The alternatives (2, 3 and 4) are single panel plots of time series, instantaneous velocity and instantaneous acceleration, respectively. |
ci |
numeric, enables a user defined input to select the type of confidence interval to be displayed on the plots. The default setting (ci = 1) corresponds to a 95% confidence interval whilst ci=2 provides a 99% confidence interval. |
This routine provides a range of screen plotting options for both
“msl.trend” (see msl.trend) and “msl.forecast”
(see msl.forecast) objects. The same range of alternative pdf
plotting options are available via msl.pdf.
msl.trend, msl.forecast,
msl.pdf, Balt, s, t
# ------------------------------------------------------------------------- # Isolate trend from Baltimore record, filling gaps with spline interpolation, # 500 iterations and adding 1000 mm of slr to 2100. Use raw 'Balt.csv' data file. # Note: ordinarily user would call 'File.csv' direct from working directory # using the following sample code: # s <- msl.trend('Balt.csv', fillgaps = 3, iter = 500, 'BALTIMORE, USA') # t <- msl.forecast(s, slr = 1000) # ------------------------------------------------------------------------- data(s) # msl.trend object from above-mentioned example data(t) # msl.forecast object from above-mentioned example msl.plot(s) # default screen plot output, 3 panels, 95% confidence intervals msl.plot(s, type = 2) # plot time series, 95% confidence intervals msl.plot(s, type = 3) # plot instantaneous velocity, 95% confidence intervals msl.plot(s, type = 4, ci = 2) # plot acceleration, 99% confidence intervals msl.plot(t) # default screen plot output, 3 panels, 95% confidence intervals msl.plot(t, type = 2) # plot time series, 95% confidence intervals msl.plot(t, type = 3) # plot instantaneous velocity, 95% confidence intervals msl.plot(t, type = 4, ci = 2) # plot acceleration, 99% confidence intervals# ------------------------------------------------------------------------- # Isolate trend from Baltimore record, filling gaps with spline interpolation, # 500 iterations and adding 1000 mm of slr to 2100. Use raw 'Balt.csv' data file. # Note: ordinarily user would call 'File.csv' direct from working directory # using the following sample code: # s <- msl.trend('Balt.csv', fillgaps = 3, iter = 500, 'BALTIMORE, USA') # t <- msl.forecast(s, slr = 1000) # ------------------------------------------------------------------------- data(s) # msl.trend object from above-mentioned example data(t) # msl.forecast object from above-mentioned example msl.plot(s) # default screen plot output, 3 panels, 95% confidence intervals msl.plot(s, type = 2) # plot time series, 95% confidence intervals msl.plot(s, type = 3) # plot instantaneous velocity, 95% confidence intervals msl.plot(s, type = 4, ci = 2) # plot acceleration, 99% confidence intervals msl.plot(t) # default screen plot output, 3 panels, 95% confidence intervals msl.plot(t, type = 2) # plot time series, 95% confidence intervals msl.plot(t, type = 3) # plot instantaneous velocity, 95% confidence intervals msl.plot(t, type = 4, ci = 2) # plot acceleration, 99% confidence intervals
Isolate trend component from mean sea level records.
msl.trend(file, station_name = " ", fillgaps = 1, iter = 10000, plot = TRUE)msl.trend(file, station_name = " ", fillgaps = 1, iter = 10000, plot = TRUE)
file |
csv format input file with no header row of annual average water levels. This file must contain 2 columns with the first column the time period (in years) and the second column annual average ocean water levels (in millimetres). Missing data must be denoted by “NA”. Missing data and maximum missing data gap are limited to 15% and 5%, respectively, of the data record. The minimum length data record processed by the package is 80 years. Warning: If input data files do not conform to these pre-conditions, the analysis will be terminated. It should be further noted that the existence of quasi 60 year oscillations in global mean sea level have been well recognised in the literature. Therefore, in order to be effective for climate change and sea level research, only input files with a minimum length exceeding 80 years have been considered in order that the package can identify and isloate such signals. |
station_name |
character string, providing the name of the data record. Note: This field can be left blank, however, it is retained for use in banner labelling of all plotting and pdf outputs. |
fillgaps |
numeric, provides 3 alternative gap filling procedures for
missing data. The default procedure (fillgaps = 1) is based on iterative gap
filling using Singular Spectrum Analysis (refer Note: Gap filled portions of the time series are denoted in red on the default screen plot. This is done specifically to provide ready visual observation to discern if the selected gap filling method provides an appropriate estimate within the gaps in keeping with the remainder of the historical record. Depending on the nature of the record and extent of gaps, some trial and error between alternatives might be necessary to optimise gap filling. |
iter |
numeric, enables a user defined number of iterations for bootstrapping to determine error margins. The user range is [500 to 10000] where 10000 is the default setting. Warning: Although the default setting provides a more accurate basis for estimating error margins, the degree of iterations slows the analysis and can take several minutes to run. |
plot |
logical, if ‘TRUE’ then the original time series is plotted to the screen along with the trend component and the result of gap filling (where necessary). 95% confidence intervals have also been applied. Default = TRUE. |
This is the key entry point to the package. This function deconstructs annual average time series data into a trend and associated real-time velocities and accelerations, filling necessary internal structures to facilitate all other functions in this package. The trend is isloated using Singular Spectrum Analysis, in particular, aggregating components whose low frequency band [0 to 0.01] exceed a threshold contribution of 75%. Associated velocities and accelerations are determined through the fitting of a cubic smoothing spline to the trend with 1 degree of freedom per every 8 years of record length. Refer Watson (2016a,b) for more detail.
An object of class “msl.trend” is returned with the following elements:
the name of the data record.
a summary data frame of the relevant attributes relating to the trend and the inputted annual average data set, including:
$Year: input data;
$MSL: input data;
$Trend: mean sea level trend;
$TrendSD: standard deviation of the determined mean sea level trend;
$Vel: velocity (or first derivative) of mean sea level trend (mm/year);
$VelSD: standard deviation of the velocity of the mean sea level trend;
$Acc: acceleration (or second derivative) of mean sea level trend (mm/year/year);
$AccSD: standard deviation of the acceleration of the mean sea level trend;
$Resids: time series of uncorrelated residuals; and
$FilledTS: gap-filled time series (where necessary).
outputs of the peak velocity and the year in which it occurred.
outputs of the peak acceleration and the year in which it occurred.
outputs details of the start, end and length of the input data set.
outputs the extent of missing data (years) in the original record and the gap filling method used (where necessary).
outputs the number of iterations used to generate the respective standard deviations for error margins.
outputs the number and time at which changepoints in the variance of the uncorrelated residuals occur (if any). Where changepoints are identified, block bootstrapping procedures are used with residuals quarantined between changepoints.
Watson, P.J., 2016a. Identifying the best performing time series analytics for sea-level research. In: Time Series Analysis and Forecasting, Contributions to Statistics, ISBN 978-3-319-28725-6, Springer International Publishing (in press).
Watson, P.J., 2016b. How to improve estimates of real-time acceleration in the mean sea level signal. In: Vila-Concejo, A., Bruce, E., Kennedy, D.M., and McCarroll, R.J. (eds.), Proceedings of the 14th International Coastal Symposium (Sydney, Australia). Journal of Coastal Research, Special Issue, No. 75. Coconut Creek (Florida), ISSN 0749-0208 (in press).
msl.forecast, msl.plot,
msl.pdf, summary, Balt, s.
# ------------------------------------------------------------------------- # Isolate trend from Baltimore record, filling gaps with spline interpolation and # 500 iterations. Use raw 'Balt.csv' data file. Note: ordinarily user would call # 'File.csv' direct from working directory using the following sample code: # s <- msl.trend('Balt.csv', fillgaps = 3, iter = 500, 'BALTIMORE, USA') # DONT RUN # ------------------------------------------------------------------------- data(s) # msl.trend object from above-mentioned example str(s) # check structure of msl.trend object msl.plot(s, type=2) # check screen output of gapfilling and trend estimate# ------------------------------------------------------------------------- # Isolate trend from Baltimore record, filling gaps with spline interpolation and # 500 iterations. Use raw 'Balt.csv' data file. Note: ordinarily user would call # 'File.csv' direct from working directory using the following sample code: # s <- msl.trend('Balt.csv', fillgaps = 3, iter = 500, 'BALTIMORE, USA') # DONT RUN # ------------------------------------------------------------------------- data(s) # msl.trend object from above-mentioned example str(s) # check structure of msl.trend object msl.plot(s, type=2) # check screen output of gapfilling and trend estimate
The 'msltrend' package provides improved estimates of trend (mean sea level) and associated real-time velocities and accelerations from long (minimum 80 years), individual, annual average ocean water level data records. Improved trend estimates are based on Singular Spectrum Analysis methods. Various gap-filling options are included to accommodate incomplete time series records. The package also contains a forecasting module to consider the implication of user defined quantum of sea level rise between the end of the available historical record and the year 2100. A wide range of screen and pdf plotting options are available within the package.
The msl.trend function is the key entry point to the package
deconstructing annual average time series data records into a trend and
associated real-time velocities and accelerations, filling necessary internal
structures which facilitate all functions in this package (Refer Watson 2016a,b
for more detail).
The msl.forecast function enables a user defined quantum of sea
level rise to be added from the end of the deconstructed historical record to
the year 2100. Similalrly, this function estimates real-time velocities and
accelerations from the start of the available historical record to the year 2100.
Watson, P.J., 2016a. Identifying the best performing time series analytics for sea-level research. In: Time Series Analysis and Forecasting, Contributions to Statistics, ISBN 978-3-319-28725-6, Springer International Publishing (in press).
Watson, P.J., 2016b. How to improve estimates of real-time acceleration in the mean sea level signal. In: Vila-Concejo, A., Bruce, E., Kennedy, D.M., and McCarroll, R.J. (eds.), Proceedings of the 14th International Coastal Symposium (Sydney, Australia). Journal of Coastal Research, Special Issue, No. 75. Coconut Creek (Florida), ISSN 0749-0208 (in press).
Output of call to msl.trend used extensively in examples throughout
this Manual.
data(s)data(s)
msl.trend object
This msl.trend object is used extensively in the
examples throughout this manual in order to call the object direct rather than
producing the same via original code which can be computationally expensive. This
object results from a decomposition of the Baltimore record, filling gaps with
spline interpolation and using 500 iterations to generate error margins via
bootstrapping.
Note: Ordinarily the user would call 'File.csv' direct from working directory, creating the 'msl.trend' object using the following sample code:
s <- msl.trend('Balt.csv', fillgaps = 3, iter = 500, 'BALTIMORE, USA') # DON'T RUN
msl.trend, msl.forecast,
msl.plot, msl.pdf, summary,
Balt.
data(s) str(s) # check structure of objectdata(s) str(s) # check structure of object
Summary outputs of decomposed time series.
summary(object)summary(object)
object |
of class “msl.trend” (see |
This routine provides a screen summary of the respective outputs
from a msl.trend or msl.forecast object. The
summary produced is identical to str( ) for an object of class
“msl.trend” (see msl.trend) or “msl.forecast”
(see msl.forecast).
msl.trend, msl.forecast,
Balt, s, t.
# ------------------------------------------------------------------------- # Isolate trend from Baltimore record, filling gaps with spline interpolation, # 500 iterations and adding 1000 mm of slr to 2100. Use raw 'Balt.csv' data file. # Note: ordinarily user would call 'File.csv' direct from working directory # using the following sample code: # s <- msl.trend('Balt.csv', fillgaps = 3, iter = 500, 'BALTIMORE, USA') # t <- msl.forecast(s, slr = 1000) # ------------------------------------------------------------------------- data(s) # msl.trend object from above-mentioned example data(t) # msl.forecast object from above-mentioned example summary(s) # summary for object of class 'msl.trend' object summary(t) # summary for object of class 'msl.forecast' object# ------------------------------------------------------------------------- # Isolate trend from Baltimore record, filling gaps with spline interpolation, # 500 iterations and adding 1000 mm of slr to 2100. Use raw 'Balt.csv' data file. # Note: ordinarily user would call 'File.csv' direct from working directory # using the following sample code: # s <- msl.trend('Balt.csv', fillgaps = 3, iter = 500, 'BALTIMORE, USA') # t <- msl.forecast(s, slr = 1000) # ------------------------------------------------------------------------- data(s) # msl.trend object from above-mentioned example data(t) # msl.forecast object from above-mentioned example summary(s) # summary for object of class 'msl.trend' object summary(t) # summary for object of class 'msl.forecast' object
Output of call to msl.forecast used extensively in examples throughout
this Manual.
data(t)data(t)
msl.forecast object
This msl.forecast object is used extensively in the
examples throughout this manual in order to call the object direct rather than
producing the same via original code which can be computationally expensive. This
object results from a decomposition of the Baltimore record, filling gaps with
spline interpolation and using 500 iterations to generate error margins via
bootstrapping (see s). This 'msl.trend' object is then parsed to
msl.forecast with the addition of 1000 millimetres of sea level rise
between the end of the historical record and 2100.
Note: Ordinarily the user would call 'File.csv' direct from working
directory, creating the 'msl.trend' object first, then creating the above-mentioned
msl.forecast object using the following sample code:
s <- msl.trend('Balt.csv', fillgaps = 3, iter = 500, 'BALTIMORE, USA') # DON'T RUN
t <- msl.forecast(s, slr = 1000) # DON'T RUN
msl.trend, msl.forecast,
msl.plot, msl.pdf, summary,
Balt, s.
data(t) str(t) # check structure of objectdata(t) str(t) # check structure of object