The fit is done in terms of sine and cosine components at the indicated tidal frequencies, with the amplitude and phase being calculated from the resultant coefficients on the sine and cosine terms.
tidem(t, x, constituents, latitude = NULL, rc = 1, regress = lm,
debug = getOption("oceDebug"))Either a sealevel object (e.g. produced by
read.sealevel or as.sealevel) or a vector of
times. In the former case, time is part of the object, so t may not
be given here. In the latter case, tidem needs a way to determine
time, so t must be given.
an optional numerical vector holding something that varies with
time. This is ignored if t is a sealevel-class object,
in which case it is inferred as t[["elevation"]].
an optional list of tidal constituents to which the fit is done (see “Details”.)
if provided, the latitude of the observations. If not
provided, tidem will try to infer this from sl.
the value of the coefficient in the Rayleigh criterion.
function to be used for regression, by default
lm, but could be for example rlm from the
MASS package.
an integer specifying whether debugging information is
to be printed during the processing. This is a general parameter that
is used by many oce functions. Generally, setting debug=0
turns off the printing, while higher values suggest that more information
be printed. If one function calls another, it usually reduces the value of
debug first, so that a user can often obtain deeper debugging
by specifying higher debug values.
An object of tidem-class, consisting of
constituent number, e.g. 1 for Z0, 1 for SA,
etc.
the regression model
a vector of constituent
names, in non-subscript format, e.g. "M2".
a vector of constituent frequencies, in inverse hours.
a vector of fitted constituent amplitudes, in metres.
a vector of fitted constituent phase. NOTE: The definition of phase is likely to change as this function evolves. For now, it is phase with respect to the first data sample.
a vector containing a sort of p value for each constituent. This is calculated as the average of the p values for the sine() and cosine() portions used in fitting; whether it makes any sense is an open question.
1.This function is not fully developed yet, and both the form of the call and the results of the calculation may change.
2.Nodal correction is not done.
3.The reported p value may make no sense at all, and it might be
removed in a future version of this function. Perhaps a significance level
should be presented, as in the software developed by both Foreman and
Pawlowicz.
The tidal constituents to be used in the analysis are specified as follows.
Case 1. If constituents is not provided, then the constituent
list will be made up of the 69 constituents regarded by Foreman as standard.
These include astronomical frequencies and some shallow-water frequencies,
and are as follows: c("Z0", "SA", "SSA", "MSM", "MM", "MSF", "MF",
"ALP1", "2Q1", "SIG1", "Q1", "RHO1", "O1", "TAU1", "BET1", "NO1", "CHI1",
"PI1", "P1", "S1", "K1", "PSI1", "PHI1", "THE1", "J1", "SO1", "OO1", "UPS1",
"OQ2", "EPS2", "2N2", "MU2", "N2", "NU2", "GAM2", "H1", "M2", "H2", "MKS2",
"LDA2", "L2", "T2", "S2", "R2", "K2", "MSN2", "ETA2", "MO3", "M3", "SO3",
"MK3", "SK3", "MN4", "M4", "SN4", "MS4", "MK4", "S4", "SK4", "2MK5", "2SK5",
"2MN6", "M6", "2MS6", "2MK6", "2SM6", "MSK6", "3MK7", "M8").
Case 2. If the first item in constituents is the string
"standard", then a provisional list is set up as in Case 1, and then
the (optional) rest of the elements of constituents are examined, in
order. Each of these constituents is based on the name of a tidal
constituent in the Foreman (1977) notation. (To get the list, execute
data(tidedata) and then execute cat(tideData$name).) Each
named constituent is added to the existing list, if it is not already there.
But, if the constituent is preceeded by a minus sign, then it is removed
from the list (if it is already there). Thus, for example,
constituents=c("standard", "-M2", "ST32") would remove the M2
constituent and add the ST32 constituent.
Case 3. If the first item is not "standard", then the list of
constituents is processed as in Case 2, but without starting with the
standard list. As an example, constituents=c("K1", "M2") would fit
for just the K1 and M2 components. (It would be strange to use a minus sign
to remove items from the list, but the function allows that.)
In each of the above cases, the list is reordered in frequency prior to the
analysis, so that the results of summary,tidem-method will be in a
familiar form.
Once the constituent list is determined, tidem prunes the elements of
the list by using the Rayleigh criterion, according to which two
constituents of frequencies \(f_1\) and \(f_2\) cannot be
resolved unless the time series spans a time interval of at least
\(rc/(f_1-f_2)\). The value rc=1 yields nominal
resolution.
A specific example may be of help in understanding the removal of unresolvable
constitutents. For example, the data(sealevel) dataset is of length
6718 hours, and this is too short to resolve the full list of constituents,
with the conventional (and, really, necessary) limit of rc=1.
From Table 1 of [1], this timeseries is too short to resolve the
SA constituent, so that SA will not be in the resultant.
Similarly, Table 2 of [1] dictates the removal of
PI1, S1 and PSI1 from the list. And, finally,
Table 3 of [1] dictates the removal of
H1, H2, T2 and R2. Also, since Table 3
of [1] indiates that GAM2 gets subsumed into H1,
and if H1 is already being deleted in this test case, then
GAM2 will also be deleted.
A list of constituent names is created by the following:
data(tidedata) print(tidedata$const$name)
The text should include discussion of the (not yet performed) nodal correction treatment.
1. Foreman, M. G. G., 1977. Manual for tidal heights analysis and prediction. Pacific Marine Science Report 77-10, Institute of Ocean Sciences, Patricia Bay, Sidney, BC, 58pp.
2. Foreman, M. G. G., Neufeld, E. T., 1991. Harmonic tidal analyses of long time series. International Hydrographic Review, 68 (1), 95-108.
3. Leffler, K. E. and D. A. Jay, 2009. Enhancing tidal harmonic analysis: Robust (hybrid) solutions. Continental Shelf Research, 29(1):78-88.
4. Pawlowicz, Rich, Bob Beardsley, and Steve Lentz, 2002. Classical tidal
harmonic analysis including error estimates in MATLAB using T_TIDE.
Computers and Geosciences, 28, 929-937.
Other things related to tidem data: [[,tidem-method,
[[<-,tidem-method,
plot,tidem-method,
predict.tidem,
summary,tidem-method,
tidedata, tidem-class,
tidemAstron, tidemVuf
# NOT RUN {
library(oce)
# The demonstration time series from Foreman (1977),
# also used in T_TIDE (Pawlowicz, 2002).
data(sealevelTuktoyaktuk)
tide <- tidem(sealevelTuktoyaktuk)
summary(tide)
# AIC analysis
extractAIC(tide[["model"]])
# Fake data at M2
t <- seq(0, 10*86400, 3600)
eta <- sin(0.080511401 * t * 2 * pi / 3600)
sl <- as.sealevel(eta)
m <- tidem(sl)
summary(m)
# }
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