Convert ADP velocity components from a xyz-based coordinate system to
an enu-based coordinate system, by using the instrument's recording of
information relating to heading, pitch, and roll. The action is based
on what is stored in the data, and so it depends greatly on instrument type
and the style of original data format. This function handles data from
RDI Teledyne, Sontek, and some Nortek instruments directly. However, Nortek
data stored in in the AD2CP format are handled by the specialized
function `xyzToEnuAdpAD2CP()`

, the documentation for which
should be consulted, rather than the material given blow.

xyzToEnuAdp(x, declination = 0, debug = getOption("oceDebug"))

x | an adp object. |
---|---|

declination | magnetic declination to be added to the heading after "righting" (see below), to get ENU with N as "true" north. |

debug | an integer specifying whether debugging information is
to be printed during the processing. This is a general parameter that
is used by many |

An object with `data$v[,,1:3]`

altered appropriately, and
`x[["oceCoordinate"]]`

changed from `xyz`

to `enu`

.

The first step is to convert the (x,y,z) velocity components (stored in the
three columns of `x[["v"]][,,1:3]`

) into what RDI (reference 1, pages 11 and 12)
calls "ship" (or "righted") components. For example, the z coordinate,
which may point upwards or downwards depending on instrument orientation, is
mapped onto a "mast" coordinate that points more nearly upwards than
downward. The other ship coordinates are called "starboard" and "forward",
the meanings of which will be clear to mariners. Once the (x,y,z)
velocities are converted to ship velocities, the orientation of the
instrument is extracted from heading, pitch, and roll vectors stored in the
object. These angles are defined differently for RDI and Sontek profilers.

The code handles every case individually, based on the table given below. The table comes from Clark Richards, a former PhD student at Dalhousie University (reference 2), who developed it based on instrument documentation, discussion on user groups, and analysis of measurements acquired with RDI and Sontek acoustic current profilers in the SLEIWEX experiment. In the table, (X, Y, Z) denote instrument-coordinate velocities, (S, F, M) denote ship-coordinate velocities, and (H, P, R) denote heading, pitch, and roll.

Case | Mfr. | Instr. Orient. | H | P | R | S | F | M | 1 | RDI | ADCP |

up | H | arctan(tan(P)*cos(R)) | R | -X | Y | -Z | 2 | RDI | ADCP | down | H |

arctan(tan(P)*cos(R)) | -R | X | Y | Z | 3 | Nortek | ADP | up | H-90 | R | -P |

X | Y | Z | 4 | Nortek | ADP | down | H-90 | R | -P | X | -Y |

-Z | 5 | Sontek | ADP | up | H-90 | -P | -R | X | Y | Z | 6 |

Sontek | ADP | down | H-90 | -P | -R | X | Y | Z | 7 | Sontek | PCADP |

up | H-90 | R | -P | X | Y | Z | 8 | Sontek | PCADP | down | H-90 |

Finally, a standardized rotation matrix is used to convert from ship
coordinates to earth coordinates. As described in the RDI coordinate
transformation manual (reference 1, pages 13 and 14), this matrix is based on sines
and cosines of heading, pitch, and roll If `CH`

and `SH`

denote
cosine and sine of heading (after adjusting for declination), with similar
terms for pitch and roll using second letters `P`

and `R`

, the
rotation matrix is

rbind(c( CH*CR + SH*SP*SR, SH*CP, CH*SR - SH*SP*CR), c(-SH*CR + CH*SP*SR, CH*CP, -SH*SR - CH*SP*CR), c( -CP*SR, SP, CP*CR))

This matrix is left-multiplied by a matrix with three rows, the top a vector
of "starboard" values, the middle a vector of "forward" values, and the
bottom a vector of "mast" values. Finally, the columns of
`data$v[,,1:3]`

are filled in with the result of the matrix
multiplication.

Teledyne RD Instruments. “ADCP Coordinate Transformation: Formulas and Calculations,” January 2010. P/N 951-6079-00.

Clark Richards, 2012, PhD Dalhousie University Department of Oceanography.

Other things related to adp data:
`[[,adp-method`

,
`[[<-,adp-method`

,
`ad2cpHeaderValue()`

,
`adp-class`

,
`adpEnsembleAverage()`

,
`adp_rdi.000`

,
`adp`

,
`as.adp()`

,
`beamName()`

,
`beamToXyzAdpAD2CP()`

,
`beamToXyzAdp()`

,
`beamToXyzAdv()`

,
`beamToXyz()`

,
`beamUnspreadAdp()`

,
`binmapAdp()`

,
`enuToOtherAdp()`

,
`enuToOther()`

,
`handleFlags,adp-method`

,
`is.ad2cp()`

,
`plot,adp-method`

,
`read.adp.ad2cp()`

,
`read.adp.nortek()`

,
`read.adp.rdi()`

,
`read.adp.sontek.serial()`

,
`read.adp.sontek()`

,
`read.adp()`

,
`read.aquadoppHR()`

,
`read.aquadoppProfiler()`

,
`read.aquadopp()`

,
`rotateAboutZ()`

,
`setFlags,adp-method`

,
`subset,adp-method`

,
`subtractBottomVelocity()`

,
`summary,adp-method`

,
`toEnuAdp()`

,
`toEnu()`

,
`velocityStatistics()`

,
`xyzToEnuAdpAD2CP()`

,
`xyzToEnu()`