scientimate.pressure2surfaceelevfft#

Eta, t = scientimate.pressure2surfaceelevfft(P, fs, duration, h, heightfrombed=0, fmaxpcorr=None, fminpcorr=0, fcL=0, fcH=None, fmaxpcorrCalcMethod='auto', Kpafterfmaxpcorr='constant', kCalcMethod='beji', Rho=1000, dispout='no')

Description#

Calculate water surface elevation time series from water pressure time series by using Fast Fourier Transform

Inputs#

P: Water pressure time series data in (N/m^2)
fs: Sampling frequency that data collected at in (Hz)
duration: Duration time that data are collected (second)
h: Water depth in (m)
heightfrombed=0: Height from bed that data collected at in (m)
fmaxpcorr=fs/2: Maximum frequency that a pressure attenuation factor applies up on that (Hz)

If fmaxpcorrCalcMethod=’user’, then the smaller of calculated and user defined fmaxpcorr will be chosen
fminpcorr=0: Minimum frequency that is used for defining fmaxpcorr if fmaxpcorrCalcMethod=’auto’ (Hz)

fminpcorr should be smaller than fp

If swell energy exists, fminpcorr should be smaller than fp of wind sea (fpsea) and larger than fp of swell (fpswell) if there swell
fcL=0: Low cut-off frequency, between 0*fs to 0.5*fs (Hz)
fcH=fs/2: High cut-off frequency, between 0*fs to 0.5*fs (Hz)
fmaxpcorrCalcMethod=’auto’: Define if to calculate fmaxpcorr and ftail or to use user defined

‘user’: use user defined value for fmaxpcorr

‘auto’: automatically define value for fmaxpcorr
Kpafterfmaxpcorr=’constant’: Define a pressure response factor, Kp, value for frequency larger than fmaxpcorr

‘nochange’: Kp is not changed for frequency larger than fmaxpcorr

‘one’: Kp=1 for frequency larger than fmaxpcorr

‘constant’: Kp for f larger than fmaxpcorr stays equal to Kp at fmaxpcorr (constant)
kCalcMethod=’beji’: Wave number calculation method

‘hunt’: Hunt (1979), ‘beji’: Beji (2013), ‘vatankhah’: Vatankhah and Aghashariatmadari (2013)

‘goda’: Goda (2010), ‘exact’: calculate exact value
Rho=1000: Water density (kg/m^3)
dispout=’no’: Define to display outputs or not (‘yes’: display, ‘no’: not display)

Outputs#

Eta: Water surface elevation time series in (m)
t: Time (s)

Examples#

import scientimate as sm
import numpy as np
import scipy as sp
from scipy import signal

fs=2 #Sampling frequency
duration=1024 #Duration of the data
N=fs*duration #Total number of points
df=fs/N #Frequency difference
dt=1/fs #Time difference, dt=1/fs
t=np.linspace(0,duration-dt,N) #Time
Eta=sp.signal.detrend(0.5*np.cos(2*np.pi*0.2*t)+(-0.1+(0.1-(-0.1)))*np.random.rand(N))
hfrombed=4
h=5
k=0.2
P=Eta*9.81*1000*(np.cosh(k*hfrombed)/np.cosh(k*h))
Eta,t=sm.pressure2surfaceelevfft(P,fs,duration,5,4,0.7,0.15,0,fs/2,'auto','constant','beji',1025,'yes')

References#

Beji, S. (2013). Improved explicit approximation of linear dispersion relationship for gravity waves. Coastal Engineering, 73, 11-12.

Goda, Y. (2010). Random seas and design of maritime structures. World scientific.

Hunt, J. N. (1979). Direct solution of wave dispersion equation. Journal of the Waterway Port Coastal and Ocean Division, 105(4), 457-459.

Vatankhah, A. R., & Aghashariatmadari, Z. (2013). Improved explicit approximation of linear dispersion relationship for gravity waves: A discussion. Coastal engineering, 78, 21-22.

Welch, P. (1967). The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Transactions on audio and electroacoustics, 15(2), 70-73.

scientimate.pressure2surfaceelevfft

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