tidem {oce} | R Documentation

## 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. 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.

### 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")`.

2. 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.

3. 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 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.

### Value

An object of `tidem-class`, consisting of

`const` | constituent number, e.g. 1 for `Z0`, 1 for `SA`, etc.
`model` | the regression model
`name` | a vector of constituent names, in non-subscript format, e.g. "`M2`".
`frequency` | a vector of constituent frequencies, in inverse hours.
`amplitude` | a vector of fitted constituent amplitudes, in metres.
`phase` | 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.
`p` | 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.

### 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.

### Author(s)

Dan Kelley

### 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)

[Package oce version 0.9-22 Index]