oce (version 0.9-20)

tidem: Fit a Tidem (Tidal Model) to a Timeseries

Description

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.

Usage

tidem(t, x, constituents, latitude = NULL, rc = 1, regress = lm, debug = getOption("oceDebug"))

Arguments

t

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.

x

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"]].

constituents

an optional list of tidal constituents to which the fit is done (see “Details”.)

latitude

if provided, the latitude of the observations. If not provided, tidem will try to infer this from sl.

rc

the value of the coefficient in the Rayleigh criterion.

regress

function to be used for regression, by default lm, but could be for example rlm from the MASS package.

debug

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.

Value

An object of tidem-class, consisting of , consisting of

Bugs

1. 1.This function is not fully developed yet, and both the form of the call and the results of the calculation may change.
2. 2.Nodal correction is not done.
3. 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.

Details

The tidal constituents to be used in the analysis are specified as follows.

1. 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 $f1$ and $f2$ cannot be resolved unless the time series spans a time interval of at least $rc/(f1-f2)$. The value rc=1 yields nominal resolution.

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 treatement.

References

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.

See Also

Other things related to tidem data: [[,tidem-method, [[<-,tidem-method, plot,tidem-method, predict.tidem, summary,tidem-method, tidedata, tidem-class, tidemAstron, tidemVuf

Examples

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)