```
#' Correct for depth attenuation of a water surface height
#' pressure signal.
#'
#' Bottom-mounted pressure transducers suffer from pressure signal
#' attenuation when attempting to estimate surface wave heights. This
#' function corrected water surface height time series based on the
#' depth of the water column and height of the sensor above the bottom.
#'
#' @param pt A vector of water surface heights (units of meters usually).
#' @param Fs Sampling frequency (units of Hz). Normally 4Hz for an OWHL logger.
#' @param zpt Height of the pressure sensor above the seabed (units of meters).
#' @param M Length of time series segments that will be used in the detrending
#' and attenuation correction operations. 512 samples is the default, should be
#' an even number.
#' @param CorrLim [min max] frequency for attenuation correction (Hz, optional,
#' default [0.05 0.33]).
#' @return A vector of the depth-corrected surface heights (units of meters
#' usually). Any original trend in the input data (such as tide change) is
#' present in the output data. The returned surface height fluctuations will
#' typically be more extreme than the raw input surface heights.
#' @references Original MATLAB function by Urs Neumeier
#' http://neumeier.perso.ch/matlab/waves.html Modified from the Pcorr3.m
#' function written by T. Mason, SOC, January 1997
#'
#'
#' Each segment of pt will be linearly detrended, corrected for attenuation,
#' and the linear trend will be added back to the returned data.
#' @export
#' @examples
#' data(wavedata)
#' corrected = prCorr(wavedata$SurfaceHeightRaw.m, Fs = 4, zpt = 0.1)
#' # Plot the results
#' plot(x = wavedata$DateTime, y = corrected, type = 'l',
#' ylab='Surface Height, m', xlab = 'Time')
#' lines(x = wavedata$DateTime, y = wavedata$SurfaceHeightRaw.m, col = 'red')
#' legend('topleft',legend=c('Corrected','Raw'),col=c('black','red'),lwd = 2)
prCorr <- function(pt, Fs, zpt, M = 512, CorrLim = c(0.05, 0.33), plot = FALSE ){
# Normally the maximum attenuation correction should not be higher than 5
max_attenuation_correction <- 5
# % higher value to process boat-waves for Jean Ellis
# % max_attenuation_correction <- 20;
# Minimum frequency, below which no correction is applied
# (0.05) = 20 s period
min_frequency <- CorrLim[1]
# Maximum frequency, above which no correction is applied
# (0.33) = 3 s period
max_frequency <- CorrLim[2]
# Make a copy of the input depth values
H_with_NaN <- pt
# Get the indices of good data (not NA)
notNA <- which( !is.nan(pt) )
# Make a reduced copy with only the good rows of pt
pt<-pt[notNA]
do_detrend <- TRUE # Need to insert code to check for presence of
# an argument 'h', h and skip the detrending if it
# was provided. LPM note: h is not currently an argument
m <- length(pt) # m = number of samples (all the NAs are excluded)
Noverlap <- M/2 # length of overlap of segments. M is an argument to the
# function and has a default of 512
N <- ( ceiling(m/M) ) * M # length of array, will be
# zero-padded to nearest multiple of M
f <- c(NA, seq(1, (M/2), by = 1) * Fs/M)
# f will be a vector of frequencies, with a NA in the 1st position.
x <- seq(1, M, by = 1) # vector of indices from 1 to M
H <- vector(mode="numeric", length = N) # Make a vector of zeros, length N
overlap_window <- signal::hanning(M); # R version of MATLAB's hann() function,
# returns a L-point symmetric Hann window that
# is used as an array of coefficients to
# combine overlapping segments
# Mirror the overlap values in the 2nd half of overlap_window
overlap_window[((M/2)+1):length(overlap_window)] <- 1 - overlap_window[1:(M/2)]
# Step through segments of pt vector, detrend the data if needed
for (q in seq(1, N-Noverlap, by = Noverlap)){
o <- min(c(q+M-1, m))
ptseg <- pt[q:o]
seg_len <- length(ptseg)
if (do_detrend){
detrended <- oceanwaves::detrendHeight(ptseg)
trend <- detrended[['trend']][] # regression coefficients
h <- detrended[['h']][] # mean height of segment
ptseg <- detrended[['pt']][] # detrended pressure time series
seg_len <- detrended[['seg_len']] # segment length
# Calculate the wave number for each frequency in f, using the
# mean sea surface height h for this segment of data
K <- waveNumL(f,h); # waveNumL function defined separately
# Correction factor of spectrum for pressure
Kpt <- cosh(K*zpt) / cosh(K*h)
# Recall that zpt is supplied as an argument to the function,
# giving the height of the pressure transducer above the seabed.
# Set values for frequencies outside the desired range to
# 1 so that no attenuation is applied
# (i.e. attenuate 0.05-0.33Hz only)
Kpt[f < min_frequency | f > max_frequency] <- 1
Kpt[Kpt < (1/max_attenuation_correction)] <- 1 /
max_attenuation_correction
# % correction factor never higher than max_attenuation_correction
# % linear decrease of correction above f>max_frequency
fb_max <- max(which(f <= max_frequency))
# matlab fix() function rounds toward zero, R trunc() function
# should substitute
# The min() function will return the smaller of
# fb_max+fix(length(K)/10) or length(K)
mymin <- min(c(fb_max + trunc(length(K)/10), length(K)))
fKlin <- seq(fb_max, mymin, by = 1)
Kpt[fKlin] <- ((seq(length(fKlin), 1, by= -1)) *
(Kpt[fb_max]-1) / length(fKlin)) + 1
Kpt[1] <- 1 # Overwrites that NA that's been hanging out in row 1
# 2nd half of series is symmetric
Kpt[seq(M,((M/2)+2),by=-1)] <- Kpt[2:(M/2)]
} # End of if(do_detrend) statement
if (seg_len < M){
ptseg[(seg_len+1):M] <- 0 # pad ptseg with zeros if its length is
# shorter than M
}# end of if(seg_len < M)
P <- fft(ptseg) # Calculate spectrum
Pcor <- P / Kpt # Apply correction factor
# The R fft(x, inverse=TRUE) function returns unnormalized series, so it
# is necessary to divide by length(x)
# The Re() function keeps only the real part of the result
Hseg <- Re(fft(Pcor, inverse = TRUE) / length(Pcor))
# Keep only the part that is the same length as the original segment.
Hseg <- Hseg[1:seg_len]
if (do_detrend){
# Add linear regression values back on to the detrended data so that
# they are once again trended.
Hseg <- Hseg + (trend[1] + trend[2]*x[1:seg_len])
# Hseg should now contain sea surface height values (meters)
}
# Insert the corrected sea surface heights back into the vector H
# using the coefficients in overlap_window to taper the ends of the
# the segment Hseg
H[q:o] <- H[q:o] + Hseg * overlap_window[1:seg_len]
# Handle the 1st segment in H
if (q == 1){
H[1: min(c(Noverlap,seg_len))] <- Hseg[1: min(c(Noverlap,seg_len))]
}
# Deal with the tail end of H
if ( ( (q+M) >= N) & (seg_len > Noverlap)){
H[(q+Noverlap):o] <- Hseg[(Noverlap+1):length(Hseg)]
}
} # End of for (q in seq(1,N-Noverlap,by=Noverlap)) loop
H <- H[1:m] # truncate H back to original length m
# Place the new corrected heights back into the
# the positions in the original vector that had
# good data.
H_with_NaN[notNA] <- H;
# And rename that to be H
H <- H_with_NaN
if (plot) {
plot(x = wavedata$DateTime, y = H, type = 'l',
ylab='Surface Height, m', xlab = 'Time')
lines(x = wavedata$DateTime, y = wavedata$SurfaceHeightRaw.m,
col = 'red')
legend('topleft',legend=c('Corrected','Raw'),col=c('black','red'),
lwd = 2)
}
H # return H with all of the depth-corrected surface heights and the
# missing values (NA) re-inserted. Should be the same length as the input
# vector pt. Units should be the same as the original input values
# in the vector pt (usually meters).
} # end of prCorr function
#' A function to calculate wave number.
#'
#' @param f A numeric vector of wave frequencies
#' @param h A numeric vector of water depths (usually in units of meters)
#' @return The wave number.
#' @references Modified from MATLAB function by Urs Neumeier:
#' http://neumeier.perso.ch/matlab/waves.html
#' @author George Voulgaris, SUDO, 1992
waveNumL <- function(f, h) {
w <- 2 * pi * f
dum1 <- (w^2) * h / 9.81
dum2 <- dum1 +
(1.0 + 0.6522 * dum1 + 0.4622 * dum1^2 + 0.0864 * dum1^4 +
0.0675 * dum1^5)^(-1);
dum3 <- sqrt(9.81 * h * dum2^(-1)) / f
y <- 2 * pi * dum3^(-1)
y # return y
}
```

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