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, infer = NULL, 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 vector of strings that name tidal constituents to which the fit is done (see “Details” and “Constituent Naming Convention”.)
a list of constituents to be inferred from
fitted constituents according to the method outlined
in Section 2.3.4 of Foreman (1977) [1].
If infer is NULL, the default, then
no such inferences are made. Otherwise, some constituents
are computed based on other constituents, instead of being
determined by regression at the proper frequency.
If provided, infer must be a list containing
four elements:
name, a vector of strings naming the constituents to be
inferred; from, a vector of strings naming the fitted
constituents used as the sources for those inferences (these
source constituents are added to the regression list, if they
are not already there);
amp, a numerical vector of factors to be applied to the
source amplitudes; and phase, a numerical vector of angles,
in degrees, to be subtracted from the source phases. For example,
Following Foreman (1997) [1], if any of the name items
have already been computed, then the suggested inference is ignored,
and the already-computed values are used.
infer=list(name=c("P1","K2"),
from=c("K1", "S2"),
amp=c(0.33093, 0.27215),
phase=c(-7.07, -22.4)
means that the amplitude of P1 will be set as 0.33093 times the calculated amplitude
of K1, and that the P1 phase will be set to the K1 phase,
minus an offset of -7.07 degrees.
(This example is used in the Foreman (1977) [1] discussion of a
Fortran analysis code and also in Pawlowicz et al. (2002) [4] discussion
of the T_TIDE Matlab code.
Rounded to the 0.1mm resolution of values reported in [1] and [2],
the tidem results have root-mean-square amplitude difference
to Foreman's Appendix 7.3 of 0.06mm; by comparison,
the results in Table 1 of Pawlowicz et al. (2002) agree with Foreman's
results to RMS difference 0.04mm.)
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.
This function is not fully developed yet, and both the form of the call and the results of the calculation may change.
Nodal correction is not done.
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.
tidem uses constituent names that follow the convention
set by Foreman (1977) [1]. This convention is slightly different
from that used in the T-TIDE package of Pawlowicz et al.
(2002) [4], with Foreman's UPS1 and M8 becoming
UPSI and MS in T-TIDE. As a convenience,
tidem converts from these T-TIDE names to the
Foreman names, issuing warnings when doing so.
The tidem amplitude and phase results, obtained with
tidem(sealevelTuktoyaktuk, constituents=c("standard", "M10"),
infer=list(name=c("P1", "K2"),
from=c("K1", "S2"),
amp=c(0.33093, 0.27215),
phase=c(-7.07, -22.40))),
are identical the T_TIDE values listed in
Table 1 of Pawlowicz et al. (2002),
after rounding amplitude and phase to 4 and 2 digits past
the decimal place, to match the format of the table.
The tidal constituents to be used in the analysis are specified as follows; see “Constituent Naming Convention”.
Case 1. If constituents is not provided, then the constituent
list will be made up of the 69 constituents designated 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 preceded 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
\(rc/(f_1-f_2)\).
Finally, tidem looks in the remaining constituent list to check
that the application of the Rayleigh criterion has not removed any of the
constituents specified directly in the constituents argument. If
any are found to have been removed, then they are added back. This last
step was added on 2017-12-27, to make tidem behave the same
way as the Foreman (1977) code [1], as illustrated in his
Appendices 7.2 and 7.3. (As an aside, his Appendix 7.3 has some errors,
e.g. the frequency for the 2SK5 constituent is listed there (p58) as
0.20844743, but it is listed as 0.2084474129 in his Appendix 7.1 (p41).
For this reason, the frequency comparison is relaxed to a tol
value of 1e-7 in a portion of the oce test suite
(see tests/testthat/test_tidem.R in the source).
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] indicates 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 tides: [[,tidem-method,
[[<-,tidem-method, as.tidem,
plot,tidem-method,
predict.tidem,
summary,tidem-method,
tidedata, tidem-class,
tidemAstron, tidemVuf,
webtide
# 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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