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ray_tracer.py
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"""
Created By: Manish S. Devana ([email protected])
Ray Tracing in 4 dimensions using satGEM background fields
INSTRUCTIONS FOR RAY TRACING
1 - Load Ray Tracer as object:
Interpolation functions will be generated when during this step
2 - Set Ray Tracer object wave properties, location, and time
3 - Run raytracing with specified duration (hours) and timestep(seconds)
4 - results are return as pandas dataframe (can be easily saved as csv)
"""
import numpy as np
from scipy.integrate import solve_ivp, RK23, odeint, quad
from scipy.interpolate import RegularGridInterpolator, interp2d
import xarray as xr
from xarray import ufuncs as xru
import datetime as dt
import gsw
from ipywidgets import FloatProgress
from IPython.display import display
from numba import jit
import pandas as pd
from core_funcs import *
#-------------------------------------------------------------------------------
class raytracer(object):
"""
Integrating ray equations
Instructions:
1. Create raytracer object with initial position vector (lon, lat, depth), initial wavenumber vector (lon, lat, depth),
initial time (in format: ) and longitude /latitude /time padding (these define how big the region for making interpolation functions
2. use "run" method (i.e. raytracer.run()) to run ray tracing and store results in pandas dataframe format
Parameters:
X: Position vector (lon, lat, depth)
K: Wavenumber vector (k, l, m)
t0: initial time in pandas datetime format
lonpad:
latpad:
"""
def __init__(self, X, K, t0, lonpad=1.5, latpad=1.5, tpad=7):
"""
X = [lon, lat, z]
K = [k, l , m]
Keep Initial Conditions
"""
self.X0 = X[:]
self.K0 = K[:]
self.t0 = t0
self.p0 = .02 # random number must be assigned
self.F = gemFuncs() # generate gem functions
self.lonlim, self.latlim, self.tlim = self.F.createFuncs(
X, t0, lonpad=lonpad, latpad=latpad, tpad=tpad)
@jit
def _cgx(self, N2, Omega, K, u, f):
return ((K[0] * K[2]**2 * (N2 - f**2)) /
((K[0]**2 + K[1]**2 + K[2]**2)**2 * Omega)) + u
@jit
def _cgy(self, N2, Omega, K, v, f):
return ((K[1] * K[2]**2 * (N2 - f**2)) /
((K[0]**2 + K[1]**2 + K[2]**2)**2 * Omega)) + v
@jit
def _cgz(self, N2, Omega, K, f):
return (K[0]**2 + K[1]**2) * -K[2] * (N2 - f**2) / ((K[0]**2 + K[1]**2 + K[2]**2)**2 * Omega)
@jit
def _dKdt(self, field, K, xi, xi2, tstep):
K2 = K[0]**2 + K[1]**2 + K[2]**2
ri = 1 * (np.sqrt(field[0]) * (K[0]**2 + K[1]**2)) / (K2 * K[3])
dk = (-1 * ri * field[5] - K[0] * field[3] - K[1] * field[4]) * (tstep)
dl = (-1 * ri * field[8] - K[0] * field[6] - K[1] * field[7]) * (tstep)
dm = (-1 * ri * field[11] - K[0] * field[9] - K[1] * field[10])*(tstep)
dudt = (field[1] - self.F.U(xi))/tstep
dvdt = (field[2] - self.F.V(xi))/tstep
dndt = (np.sqrt(field[0]) - np.sqrt(self.F.N2(xi)))/tstep
# dw0 = -1 * ( K[0] * dudt + K[1] * dvdt)
dw0 = (1* (ri * (dndt) + K[0] * dudt + K[1] * dvdt))*tstep
# print(xi)
# print(xi2)
# print(dw0)
return np.array([dk, dl, dm, dw0])
def _planewave(self,t, amp, xx, yy, zz, k, l, m, omega):
return np.real((amp * \
np.exp((k*xx + l*yy + m*zz - omega*t) * -1j)))**2
def run(self, tstep=30, duration=5, lonpad=1.5, latpad=1.5,
tpad=7, direction='forward', bottom=3000,rho0=1030,
clearance =.5, shear=-.001, fname='ray_trace.csv',
strain=True,stops=True,vertspeed=True,
time_constant=False, save_data=False, progress_bar=False):
"""
INSTRUCTIONS:
TSTEP: TIMESTEP IN SECONDS (DEFAULT 30 SECONDS)
DURATION: DURATION (IN DAYS) - DEFAULT 5
IGNORE LONPAD AND LATPAD (DIDNT CHANGE FROM OLDER VERSION)
DIRECTION: "forward" and "reverse" (SETS INTEGRATION TIME DIRECTION)
BOTTOM: can set default bottom instead of using bathymetry file
Setup for midpoint method integration:
1. Get field values
2. Get Cg @ t_n, X_n
3. Get field values at t_n+dt/2, X_n + (dt/2)(Cg_n)
4. Calculate Cg @(t_n+dt/2, X_n + (dt/2)(Cg_n))
5. X_(n+1) = X_n + [dt * Cg @(t_n+dt/2, X_n + (dt/2)(Cg_n))]
"""
if direction == 'forward':
# convert duration in hours to seconds
T = np.arange(0, duration * 60 * 60, tstep)
else:
T = np.arange(0, -duration * 60 * 60, -tstep)
tstep = -tstep
Xall = []
Kall = []
amplitudes = []
energy = []
# names of all the columns in results frame
names = ('Lon', 'Lat', 'depth', 'distance','bottom_depth','k','l','m',
'omega','N2', 'U','V', 'dudx', 'dvdx', 'dndx', 'dudy',
'dvdy', 'dndy', 'dudz', 'dvdz', 'dndz','cgx','cgy','cgz',
'x','y','z', 'u0', 'v0', 'w0', 'u', 'v', 'w', 'b', 'energy',
'u_momentum', 'v_momentum', 'horiz_momentum','time' )
cg = []
steps = []
localfield = []
X = self.X0[:]
lon0 = X[0]
lat0 = X[1]
K = self.K0[:]
t0 = self.t0
allbottom = []
if progress_bar:
pbar = FloatProgress(min=0, max=T.shape[0])
pbar.value
display(pbar)
if not hasattr(self.F, 'dudx'):
lonlim, latlim, tlim = self.F.createFuncs(X, lonpad, latpad, tpad)
for ii, t1 in enumerate(T):
# Get field values
if progress_bar:
pbar.value = float(ii)
t = t0 + t1 / (24 * 60 * 60)
if X[2] > 6000:
zi1 = 2499
else:
zi1 = X[2]
f = gsw.f(X[1])
if time_constant:
t = np.copy(t0)
xi = (X[0], X[1], zi1, t)
field = self.F.getfield(xi)
f = gsw.f(X[1])
# Step 1
dy1 = self._cgy(field[0], K[3], K, field[2], f) * tstep / 2
dz1 = self._cgz(field[0], K[3], K, f) * tstep / 2
dx1 = self._cgx(field[0], K[3], K, field[1], f) * tstep / 2
# midpoint position
lon2, lat2 = inverse_hav(dx1, dy1, X[0], X[1])
if X[2] + dz1 > 6000:
zi = 2499
else:
zi = X[2] + dz1
xi2 = (lon2, lat2, zi, t + tstep / (24 * 60 * 60 * 2))
if time_constant:
xi2 = (lon2, lat2, zi, t)
field1 = self.F.getfield(xi2)
f2 = gsw.f(lat2)
# Update Wave properties at midpoint (midpoint refraction)
dK = self._dKdt(field1, K, xi, xi2, tstep/2)
if not np.all(np.isfinite(dK)):
K1 = K[:]
else:
if strain:
K1 = [K[0] + dK[0],
K[1] + dK[1],
K[2] + dK[2],
K[3] + dK[3]]
else:
K1 = [K[0] ,
K[1] ,
K[2] + (tstep/2)*(-(shear)*(K[0] + K[1])) ,
K[3] + dK[3]]
# Step2
dx2 = self._cgx(field1[0], K1[3], K1, field1[1], f2) * tstep
dy2 = self._cgy(field1[0], K1[3], K1, field1[2], f2) * tstep
dz2 = self._cgz(field1[0], K1[3], K1, f2) * tstep
lon3, lat3 = inverse_hav(dx2, dy2, X[0], X[1])
lonr = np.expand_dims(np.array([lon0, lon3]), axis=1)
latr = np.expand_dims(np.array([lat0, lat3]), axis=1)
distance = gsw.distance(lonr, latr, axis=0)
if X[2] + dz2 > 6000:
zi = 2499
bathypad = np.linspace(-.01,.01, num=5)
loncheck = bathypad + X[0]
latcheck = bathypad + X[1]
loncheck, latcheck = np.meshgrid(loncheck, latcheck)
tester = np.array([loncheck.flatten(), latcheck.flatten()])
bottom = np.nanmax([-self.F.bathy((p1[0], p1[1])) \
for p1 in tester.T])
# bottom = -self.F.bathy((X[0], X[1]))
X1 = [lon3, lat3, X[2] + dz2, distance, bottom]
steps.append([dx2, dy2, -dz2])
cg.append([dx2 / tstep, dy2 / tstep, -dz2 / tstep])
localfield.append(field)
Kall.append(K1)
K = K1
Xall.append(X1)
X = X1
dist_so_far = np.cumsum(steps, axis=0)
# print(dK[3])
# print(K[3]**2)
k = np.copy(K1[0])
l = np.copy(K1[1])
m = np.copy(K1[2])
omega = np.copy(K1[3])
f = gsw.f(lat3)
w0 = (self.p0 * (-m * omega) / (field[0] - omega**2))
# Perturbation amplitudes
u0 = (self.p0 * (k * omega + l * f * 1j) / (omega**2 - f**2))
v0 = (self.p0 * (l * omega - k * f * 1j) / (omega**2 - f**2))
b0 = (self.p0 * (-1j * m * field[0]) / (field[0] - omega**2))
# total distance so far
xx = np.copy(dist_so_far[ii, 0])
yy = np.copy(dist_so_far[ii, 1])
zz = np.copy(dist_so_far[ii, 2])
phase = k * xx + l * yy \
+ m * zz - omega * t1
# INtegration Limits
period = np.abs(2 * np.pi / omega)
t11 = t1 - period /2
t22 = t1 + period /2
# mean value theorem to get average over one wave period
u2 = .5*np.real(w0)**2
v2 = .5*np.real(v0)**2
w2 = .5*np.real(w0)**2
b2 = .5 * np.real(b0)**2
u = (quad(self._planewave, t11, t22,
args=(u0, xx, yy, zz, k, l,
m,omega))[0])
v = (quad(self._planewave, t11, t22,
args=(v0, xx, yy, zz, k, l,
m,omega))[0])
w = (quad(self._planewave, t11, t22,
args=(w0, xx, yy, zz, k, l,
m,omega))[0])
b = (quad(self._planewave, t11, t22,
args=(b0, xx, yy, zz, k, l,
m,omega))[0])
amplitudes.append([u0, v0, w0, u, v, w, b])
# Calculate U and V momentum
Umom = rho0 * (u * w)/period
Vmom = rho0 * (v * w) / period
# Calculate momentum flux
mFlux = np.sqrt(((u * w) / period)**2 + ((v * w) / period)**2)
# b = -(field[0] /omega / 9.8) * rho0 * w0 * np.sin(phase)
# Internal wave energy
E = .5 * rho0 * (u2 + v2 + w2) \
+ .5 *rho0* b2 * np.sqrt(field[0])**-2
# E =E/rho0
energy.append([E, Umom, Vmom, mFlux])
if stops:
# check if vertical speed goes to zero
if vertspeed:
if np.abs(dz2 / tstep) < 1e-4:
print('Vertical Group speed = zero {} meters from bottom'.format(bottom- X[2]))
break
if np.abs(E)> 1000:
# this checks if energy has gone to some unrealistic asymptote like behavior
print('ENERGY ERROR')
break
if ii > 3:
if np.abs(E - energy[ii - 2][0]) > .8 * E:
print('Non Linear')
break
# data Boundary checks
if not self.lonlim[0] <= X[0] <= self.lonlim[1]:
print('lon out of bounds')
break
if not self.latlim[0] <= X[1] <= self.latlim[1]:
print('lat out of bounds')
break
if not self.tlim[0] <= t <= self.tlim[1]:
print('time out of bounds')
print(t)
print(self.tlim)
break
# Check if near the bottom or surface
if X[2] + clearance*np.abs((2*np.pi)/K1[2]) >= bottom:
print('Hit Bottom - {} meters from bottom'.format(bottom- X[2]))
break
if X[2] <= 0:
print('Hit Surface')
break
# Check if frequency gets too high
if K1[3]**2 >= self.F.N2(xi2):
print('frequency above Bouyancy frequency')
# print(K[3]**2)
# print(self.F.N2(xi2))
break
if not np.isfinite(X1[0]):
print('X Update Error')
break
if np.abs(u0) < 0.0001:
print('U amplitude zero')
break
if np.abs(v0) < 0.0001:
print('v amplitude zero')
break
if np.abs(w0) < 0.0001:
print('w amplitude zero')
break
if not np.isfinite(dx1):
print('Field Error')
break
# Save data in pandas data
data = pd.DataFrame(np.concatenate(
(np.real(np.stack(Xall)),
np.real(np.stack(Kall)),
np.real(np.stack(localfield)),
np.real(np.stack(cg)),
np.real(np.stack(np.cumsum(steps, axis=0))),
np.real(np.stack(amplitudes)),
np.real(np.stack(energy)),
np.real(np.expand_dims(T[:ii + 1], axis=1))), axis=1), columns=names)
if save_data:
data.to_csv(fname)
return data