xyzToEnuAdp: Convert ADP From XYZ to ENU Coordinates

Description

Convert ADP velocity components from a xyz-based coordinate system to an enu-based coordinate system, by using the instrument's recording of heading, pitch, and roll.

Usage

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

Arguments

An adp object, i.e. one inheriting from adp-class.

declination

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

debug

a flag that turns on debugging. Set to 1 to get a moderate amount of debugging information, or to 2 to get more.

Value

An object with data$v[,,1:3] altered appropriately, and metadata$oce.orientation changed from xyz to enu.

Details

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 [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 [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 [3]. 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	R	-P	X	Y
Z	Case	Mfr.	Instr. Orient.	H	P	R	S	F	M	1

Finally, a standardized rotation matrix is used to convert from ship coordinates to earth coordinates. As described in the RDI coordinate transformation manual [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.

References

1. RD Instruments, 1998. ADCP Coordinate Transformation, formulas and calculations. P/N 951-6079-00 (July 1998).

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

3. The SLEIWEX experiment (http://myweb.dal.ca/kelley/SLEIWEX/index.php).