# This file is part of OpenDrift.
#
# OpenDrift is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, version 2
#
# OpenDrift is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with OpenDrift. If not, see <https://www.gnu.org/licenses/>.
#
# Copyright 2021, Trond Kristiansen, Niva
# Jan 2021 Simplified by Knut-Frode Dagestad, MET Norway, and adapted to to Kvile et al. (2018)
import datetime
import numpy as np
import logging; logger = logging.getLogger(__name__)
from opendrift.models.oceandrift import Lagrangian3DArray, OceanDrift
from opendrift.config import CONFIG_LEVEL_ESSENTIAL, CONFIG_LEVEL_BASIC, CONFIG_LEVEL_ADVANCED
[docs]
class LarvalFishElement(Lagrangian3DArray):
"""
Extending Lagrangian3DArray with specific properties for larval and juvenile stages of fish
"""
variables = Lagrangian3DArray.add_variables([
('diameter', {'dtype': np.float32,
'units': 'm',
'default': 0.0014}), # for NEA Cod
('neutral_buoyancy_salinity', {'dtype': np.float32,
'units': 'PSU',
'default': 31.25}), # for NEA Cod
('stage_fraction', {'dtype': np.float32, # to track percentage of development time completed
'units': '',
'default': 0.}),
('hatched', {'dtype': np.uint8, # 0 for eggs, 1 for larvae
'units': '',
'default': 0}),
('length', {'dtype': np.float32,
'units': 'mm',
'default': 0}),
('weight', {'dtype': np.float32,
'units': 'mg',
'default': 0.08}),
('survival', {'dtype': np.float32, # Not yet used
'units': '',
'default': 1.})])
[docs]
class LarvalFish(OceanDrift):
"""Buoyant particle trajectory model based on the OpenDrift framework.
Developed at MET Norway
Generic module for particles that are subject to vertical turbulent
mixing with the possibility for positive or negative buoyancy
Particles could be e.g. oil droplets, plankton, or sediments
"""
ElementType = LarvalFishElement
required_variables = {
'x_sea_water_velocity': {'fallback': 0},
'y_sea_water_velocity': {'fallback': 0},
'sea_surface_height': {'fallback': 0},
'sea_surface_wave_significant_height': {'fallback': 0},
'x_wind': {'fallback': 0},
'y_wind': {'fallback': 0},
'land_binary_mask': {'fallback': None},
'sea_floor_depth_below_sea_level': {'fallback': 100},
'ocean_vertical_diffusivity': {'fallback': 0.01, 'profiles': True},
'ocean_mixed_layer_thickness': {'fallback': 50},
'sea_water_temperature': {'fallback': 10, 'profiles': True},
'sea_water_salinity': {'fallback': 34, 'profiles': True},
'sea_surface_wave_stokes_drift_x_velocity': {'fallback': 0},
'sea_surface_wave_stokes_drift_y_velocity': {'fallback': 0},
}
def __init__(self, *args, **kwargs):
# Calling general constructor of parent class
super(LarvalFish, self).__init__(*args, **kwargs)
# IBM configuration options
self._add_config({
'IBM:fraction_of_timestep_swimming':
{'type': 'float', 'default': 0.15,
'min': 0.0, 'max': 1.0, 'units': 'fraction',
'description': 'Fraction of timestep swimming',
'level': CONFIG_LEVEL_ADVANCED},
})
self._set_config_default('drift:vertical_mixing', True)
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def update_terminal_velocity(self, Tprofiles=None,
Sprofiles=None, z_index=None):
"""Calculate terminal velocity for Pelagic Egg
according to
S. Sundby (1983): A one-dimensional model for the vertical
distribution of pelagic fish eggs in the mixed layer
Deep Sea Research (30) pp. 645-661
Method copied from ibm.f90 module of LADIM:
Vikebo, F., S. Sundby, B. Aadlandsvik and O. Otteraa (2007),
Fish. Oceanogr. (16) pp. 216-228
"""
g = 9.81 # ms-2
# Pelagic Egg properties that determine buoyancy
eggsize = self.elements.diameter # 0.0014 for NEA Cod
eggsalinity = self.elements.neutral_buoyancy_salinity
# 31.25 for NEA Cod
# prepare interpolation of temp, salt
if not (Tprofiles is None and Sprofiles is None):
if z_index is None:
z_i = range(Tprofiles.shape[0]) # evtl. move out of loop
# evtl. move out of loop
z_index = interp1d(-self.environment_profiles['z'],
z_i, bounds_error=False)
zi = z_index(-self.elements.z)
upper = np.maximum(np.floor(zi).astype(np.uint8), 0)
lower = np.minimum(upper + 1, Tprofiles.shape[0] - 1)
weight_upper = 1 - (zi - upper)
# do interpolation of temp, salt if profiles were passed into
# this function, if not, use reader by calling self.environment
if Tprofiles is None:
T0 = self.environment.sea_water_temperature
else:
T0 = Tprofiles[upper, range(Tprofiles.shape[1])] * \
weight_upper + \
Tprofiles[lower, range(Tprofiles.shape[1])] * \
(1 - weight_upper)
if Sprofiles is None:
S0 = self.environment.sea_water_salinity
else:
S0 = Sprofiles[upper, range(Sprofiles.shape[1])] * \
weight_upper + \
Sprofiles[lower, range(Sprofiles.shape[1])] * \
(1 - weight_upper)
# The density difference between a pelagic egg and the ambient water
# is regulated by their salinity difference through the
# equation of state for sea water.
# The Egg has the same temperature as the ambient water and its
# salinity is regulated by osmosis through the egg shell.
DENSw = self.sea_water_density(T=T0, S=S0)
DENSegg = self.sea_water_density(T=T0, S=eggsalinity)
dr = DENSw - DENSegg # density difference
# water viscosity
my_w = 0.001 * (1.7915 - 0.0538 * T0 + 0.007 * (T0 ** (2.0)) - 0.0023 * S0)
# ~0.0014 kg m-1 s-1
# terminal velocity for low Reynolds numbers
W = (1.0 / my_w) * (1.0 / 18.0) * g * eggsize ** 2 * dr
# check if we are in a Reynolds regime where Re > 0.5
highRe = np.where(W * 1000 * eggsize / my_w > 0.5)
# Use empirical equations for terminal velocity in
# high Reynolds numbers.
# Empirical equations have length units in cm!
my_w = 0.01854 * np.exp(-0.02783 * T0) # in cm2/s
d0 = (eggsize * 100) - 0.4 * \
(9.0 * my_w ** 2 / (100 * g) * DENSw / dr) ** (1.0 / 3.0) # cm
W2 = 19.0 * d0 * (0.001 * dr) ** (2.0 / 3.0) * (my_w * 0.001 * DENSw) ** (-1.0 / 3.0)
# cm/s
W2 = W2 / 100. # back to m/s
W[highRe] = W2[highRe]
self.elements.terminal_velocity = W
[docs]
def fish_growth(self, weight, temperature):
# Weight in milligrams, temperature in celcius
# Daily growth rate in percent according to
# Folkvord, A. 2005. "Comparison of Size-at-Age of Larval Atlantic Cod (Gadus Morhua)
# from Different Populations Based on Size- and Temperature-Dependent Growth
# Models." Canadian Journal of Fisheries and Aquatic Sciences.
# Journal Canadien Des Sciences Halieutiques # et Aquatiques 62(5): 1037-52.
GR = 1.08 + 1.79 * temperature - 0.074 * temperature * np.log(weight) \
- 0.0965 * temperature * np.log(weight) ** 2 \
+ 0.0112 * temperature * np.log(weight) ** 3
# Growth rate(g) converted to milligram weight (gr_mg) per timestep:
g = (np.log(GR / 100. + 1)) * self.time_step.total_seconds()/86400
return weight * (np.exp(g) - 1.)
[docs]
def update_fish_larvae(self):
# Hatching of eggs
eggs = np.where(self.elements.hatched==0)[0]
if len(eggs) > 0:
amb_duration = np.exp(3.65 - 0.145*self.environment.sea_water_temperature[eggs]) # Total egg development time (days) according to ambient temperature (Ellertsen et al. 1988)
days_in_timestep = self.time_step.total_seconds()/(60*60*24) # The fraction of a day completed in one time step
amb_fraction = days_in_timestep/amb_duration # Fraction of development time completed during present time step
self.elements.stage_fraction[eggs] += amb_fraction # Add fraction completed during present timestep to cumulative fraction completed
hatching = np.where(self.elements.stage_fraction[eggs]>=1)[0]
if len(hatching) > 0:
logger.debug('Hatching %s eggs' % len(hatching))
self.elements.hatched[eggs[hatching]] = 1 # Eggs with total development time completed are hatched (1)
larvae = np.where(self.elements.hatched==1)[0]
if len(larvae) == 0:
logger.debug('%s eggs, with maximum stage_fraction of %s (1 gives hatching)'
% (len(eggs), self.elements.stage_fraction[eggs].max()))
return
# Increasing weight of larvae
avg_weight_before = self.elements.weight[larvae].mean()
growth = self.fish_growth(self.elements.weight[larvae],
self.environment.sea_water_temperature[larvae])
self.elements.weight[larvae] += growth
avg_weight_after = self.elements.weight[larvae].mean()
logger.debug('Growing %s larve from average size %s to %s' %
(len(larvae), avg_weight_before, avg_weight_after))
# Increasing length of larvae, according to Folkvord (2005)
w = self.elements.weight[larvae]
self.elements.length[larvae] = np.exp(2.296 + 0.277 * np.log(w) - 0.005128 *np.log10(w)**2)
[docs]
def larvae_vertical_migration(self):
larvae = np.where(self.elements.hatched==1)[0]
if len(larvae) == 0:
return
# Vertical migration of Larvae
# Swim function from Peck et al. 2006
L = self.elements.length[larvae]
swim_speed = (0.261*(L**(1.552*L**(-0.08))) - 5.289/L) / 1000
f = self.get_config('IBM:fraction_of_timestep_swimming')
max_migration_per_timestep = f*swim_speed*self.time_step.total_seconds()
# Using here UTC hours. Should be changed to local solar time,
# although a phase shift of some hours should not make much difference
if self.time.hour < 12:
direction = -1 # Swimming down when light is increasing
else:
direction = 1 # Swimming up when light is decreasing
self.elements.z[larvae] = np.minimum(0, self.elements.z[larvae] + direction*max_migration_per_timestep)
[docs]
def update(self):
self.update_fish_larvae()
self.advect_ocean_current()
# Stokes drift
self.stokes_drift()
self.update_terminal_velocity()
self.vertical_mixing()
self.larvae_vertical_migration()