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climate.py
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climate.py
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# Climate model based off of Judy and Hansi's energy balance notebook
from bokeh.models import ColumnDataSource, WidgetBox, ColorBar
from bokeh.models.widgets import TextInput, Select, Slider, Button, Dropdown, Div
from bokeh.plotting import figure
from bokeh.models.mappers import LinearColorMapper
import bokeh.palettes as bpal
import numpy as np
import scipy.sparse as sparse
import scipy.sparse.linalg as linalg
import xarray as xr
title_style = '"text-align:left; font-weight:bold; font-size:18px"'
class PlanetClimateEBM(object):
"""
Planetary Climate class that uses the North energy balance model.
"""
def __init__(self, terra_sol_obj, plot_width=800):
energy_in = terra_sol_obj.get_planet_energy_in()
self._terra_sol = terra_sol_obj
planet_energy_in = energy_in / 4
self._plot_width = plot_width
climate_model_inputs = ColumnDataSource(
data=dict(A=[211.22], B=[2.1], Q=[planet_energy_in],
D=[1.2], S2=[-0.482], C=[9.8], nlats=[70],
tol=[1e-5], init_condition=['normal']))
self.model_input = climate_model_inputs
# Initialize EnergyBalanceModel and solve initial climate
self.planet_climate = None
self.climate_result = None
self.final_T_dataframe = None
self._update_model_and_run_sim()
# Create user inputs for EBM parameters
(self.calc_button,
self.input_wx,
(self.float_inputtext,
self.general_input)) = self.init_climate_input_wx(self.planet_climate)
def update_planet_climate(self):
self.calc_button.disabled = True
valid_float_in = {key: [float(field.value.strip())]
for key, field in self.float_inputtext.items()}
general_in = {key: [field.value]
for key, field in self.general_input.items()}
self.model_input.data.update(**valid_float_in)
self.model_input.data.update(**general_in)
self._update_model_and_run_sim()
self.calc_button.disabled = False
def _update_model_and_run_sim(self):
new_kwargs = self.get_ebm_kwargs()
self.planet_climate = EnergyBalanceModel(**new_kwargs)
self.climate_result = self.planet_climate.solve_climate()
self.final_T_dataframe = self.planet_climate.convert_1d_to_grid()
print(self.climate_result)
def _update_energy_in(self):
energy_in = self._terra_sol.get_planet_energy_in()
planet_energy_in = energy_in / 4
self.model_input.data.update(dict(Q=[planet_energy_in]))
energy_str = '{:.2f}'.format(planet_energy_in)
self.float_inputtext['Q'].value = energy_str
def init_climate_input_wx(self, planet_climate):
# Climate inputs
planet_emiss = TextInput(title='Planetary IR energy out (W/m^2)',
value='{:.2f}'.format(planet_climate.A))
planet_atm_forcing = TextInput(title='Atmosphere IR adjustment (W/m^2)',
value='{:.1f}'.format(planet_climate.B))
solar_input = TextInput(title='Incoming solar (W/m^2) [Divided by 4]',
value='{:.2f}'.format(planet_climate.Q))
energy_transport = TextInput(
title='Energy transport towards poles (1/C)',
value='{:.1f}'.format(planet_climate.D))
s2_input = TextInput(title='S2 (what is this for?)',
value='{:.3f}'.format(planet_climate.S2))
heat_capacity = TextInput(title='Planetary heat capacity (C/yr)',
value='{:.1f}'.format(planet_climate.C))
numlats = Slider(start=40, end=180, step=1, value=70,
title='Number of latitudes in model')
init_planet_T = Select(title='Initial planet temperature',
value='normal',
options=['normal', 'warm', 'cold'])
calc_climate = Button(label='Simulate Climate', button_type='success')
calc_climate.on_click(self.update_planet_climate)
refresh_energy_in = Button(label='Refresh Solar Input')
refresh_energy_in.on_click(self._update_energy_in)
float_input = {'A': planet_emiss, 'B': planet_atm_forcing,
'Q': solar_input, 'D': energy_transport,
'S2': s2_input, 'C': heat_capacity}
general_input = {'nlats': numlats,
'init_condition': init_planet_T}
clim_input_grp1 = WidgetBox(children=[planet_emiss,
planet_atm_forcing,
solar_input,
refresh_energy_in],
width=int(self._plot_width/3))
clim_input_grp2 = WidgetBox(energy_transport, s2_input, heat_capacity)
clim_input_grp3 = WidgetBox(numlats, init_planet_T)
return (calc_climate,
[clim_input_grp1, clim_input_grp2, clim_input_grp3],
(float_input, general_input))
def get_ebm_kwargs(self):
ebm_kwargs = {key: model_in[0] for key, model_in in
self.model_input.data.items()}
return ebm_kwargs
def calc_albedo(x, temperature):
a_ice = 0.6
a_noice_ocn = 0.263
a_noice_cloud = 0.04 # why is this so low?
albedo = a_ice * np.ones(len(x))
tcondition = temperature >= -2
albedo[tcondition] = a_noice_ocn + a_noice_cloud * (3*x[tcondition]**2 - 1)
return albedo
def start_conditions(nlats, condition):
temp_0 = np.ones(nlats)
if condition == 'cold':
temp_0 *= -10
elif condition == 'normal':
temp_0 *= 5
elif condition == 'warm':
temp_0 *= 15
else:
raise ValueError('Unrecognized initial condition: {}'.format(condition))
return temp_0
class EnergyBalanceModel(object):
ITERMAX = 10000
def __init__(self, A=211.22, B=2.1, Q=338.52, D=1.2, S2=-0.482, C=9.8,
nlats=70, tol=1e-5, init_condition='normal'):
self.A = A
self.B = B
self.Q = Q
self.D = D
self.S2 = S2
self.C = C
self.nlats = nlats
self.tol = tol
self.init_condition = init_condition
self.x = np.linspace(-1, 1, nlats)
self.lats = np.arcsin(self.x)
self.lats_in_deg = self.lats * 180 / np.pi
self.lons_in_deg = np.arange(0, 360, 5)
self._dx = self.x[1] - self.x[0]
self._dt = self._dx**2 / D
self.s = Q * (1 + (S2 * (3 * self.x**2 - 1) / 2))
self.T = start_conditions(nlats, init_condition)
self.T_mean = self.calc_mean_T()
self.freeze_lat = self.calc_iceline()
self.iter_T_means = None
self.iter_freeze_lat = None
self.eps = 1
self.niters = 0
def solve_climate(self):
result = ""
self.iter_T_means = []
self.iter_freeze_lat = []
dx = self._dx
dt = self._dt
term1 = self.D * (1 - self.x**2) / dx**2
term2 = self.D * self.x / (2 * dx)
for curr_iter in range(self.ITERMAX):
alpha = calc_albedo(self.x, self.T)
insolation = self.s * (1 - alpha)
# Set up tridiagonal matrix
T_p1 = np.roll(self.T, -1)
T_m1 = np.roll(self.T, 1)
diag = (self.C / self._dt) + term1 + (self.B / 2)
lodiag = -term1 / 2 - term2
updiag = -term1 / 2 + term2
mydata = [lodiag, diag, updiag]
diags = [-1, 0, 1]
TD_matrix = sparse.spdiags(mydata, diags, self.nlats, self.nlats,
format='csc')
rhs = (self.T * ((self.C / dt) - term1 - (self.B / 2)) +
T_p1 * ((term1 / 2) - term2) +
T_m1 * ((term1 / 2) + term2) - self.A + insolation)
T_new = linalg.spsolve(TD_matrix, rhs)
self.eps = np.sum(abs(self.T - T_new)**2)
self.T = T_new
self.T_mean = self.calc_mean_T()
self.freeze_lat = self.calc_iceline()
self.iter_T_means.append(self.T_mean)
self.iter_freeze_lat.append(self.freeze_lat)
self.niters = curr_iter
if self.eps <= self.tol:
break
else:
result += 'ERROR: Climate model did not converge on a solution.\n'
result += 'Final mean temperature = {:2.2f}\n'.format(
self.convert_degC_to_degF(self.T_mean))
if self.freeze_lat is not None:
result += 'Iceline latitude = {:2.1f}\n'.format(self.freeze_lat)
result += 'Number of iterations {:d}'.format(self.niters)
return result
def calc_mean_T(self):
return np.sum(np.cos(self.lats) * self.T) / np.sum(np.cos(self.lats))
def calc_iceline(self):
freezing = self.T <= -1.8
if not np.any(freezing):
# print('No freezing locations detected...')
return None
else:
freeze_lat = np.min(np.abs(self.lats_in_deg[freezing]))
return freeze_lat
@staticmethod
def convert_degC_to_degF(temp):
return temp * 9 / 5 + 32
def convert_1d_to_grid(self):
lons, lats = np.meshgrid(self.lons_in_deg, self.lats_in_deg)
values = np.ones_like(lons) * self.T[:, None]
values = values.astype(np.float32)
dataset = xr.DataArray(values, coords=[self.lats_in_deg,
self.lons_in_deg],
dims=['lat', 'lon'])
return dataset
class SimpleClimate(object):
"""
Planetary climate class that only uses albedo and a column IR opacity to
approximate surface temperature
"""
SIGMA = 5.670367e-8 # Stefan-Boltzmann Constant W.m^-2.K^-4
def __init__(self, terra_sol_obj=None, S0=1.3612e3,
plot_width=800, plot_height=400,
tau_star=0.84, f_cloud=0.7, A_cloud=0.4,
f_land=0.3, A_land=0.2):
self.title_div = Div(text="<h1>Planetary Habitability Simulator</h1>", width=plot_width)
self._terra_sol = terra_sol_obj
if terra_sol_obj is not None:
self.S0 = terra_sol_obj.get_planet_energy_in()
else:
self.S0 = S0
self.A_cloud = A_cloud
self.A_land = A_land
self.f_cloud = f_cloud
self.f_land = f_land
self.alpha = self.calc_albedo()
self.tau_star = tau_star
# Create parameter space for plot
tau_vals = np.logspace(np.log10(0.1), np.log10(150), num=300)
alpha_vals = np.linspace(0, 1, num=300)
alpha_vals, tau_vals = np.meshgrid(alpha_vals, tau_vals)
self.tau_grid = tau_vals
self.alpha_grid = alpha_vals
self.Ts = self.calc_Ts_F(tau_vals, alpha_vals)
self.plot = figure(x_range=[0, 1], y_range=[0.1, 150],
plot_width=plot_width, plot_height=plot_height,
toolbar_location='above', y_axis_type='log',
tools='box_zoom, reset')
self.img = None
self.terra_div = Div(text="", width=plot_width)
self._plot_Ts_grid()
self._update_terra_div()
self.plot.xaxis.axis_label = 'Albedo'
self.plot.yaxis.axis_label = 'Greenhouse Gas Coefficient'
self.model_wx = self.init_climate_wx()
# Lines for current selection of GHGs/albedo
self.alpha_line = self.plot.line([self.alpha, self.alpha],
[.1,150],
line_color='black',
line_width=2)
self.tau_line = self.plot.line([0,1],
[self.tau_star, self.tau_star],
line_color='black',
line_width=2)
# User's planet
self.terra_data = ColumnDataSource(data=dict(alpha=[self.alpha],
ghg_coeff=[self.tau_star],
name=['Terra'],
solar_in=[self.S0]
))
self.Terra = self.plot.circle(x='alpha', y='ghg_coeff', fill_color='burlywood',
size=20, line_color='black', legend='Terra',
source=self.terra_data)
# Points for Mars, Venus, and Earth (400 ppm CO2)
self.Earth = self.plot.circle(.3, .84, fill_color='aquamarine',
size=20, line_color='black',
legend='Earth')
# really tau*=0, but want to be visible
self.Mars = self.plot.circle(.25, 0.125, fill_color='salmon',
size=20, line_color='black',
legend='Mars')
self.Venus = self.plot.circle(.77, 125, fill_color='plum', size=20,
line_color='black',
legend='Venus')
self.plot.legend[0].background_fill_alpha = 0.5
self.plot.legend[0].location = 'bottom_left'
def init_climate_wx(self):
cloud_frac_slider = Slider(start=0, end=1, step=0.05,
value=self.f_cloud,
title='Cloud Fraction')
cloud_albedo_slider = Slider(start=0, end=1, step=0.05,
value=self.A_cloud,
title='Cloud Albedo')
land_frac_slider = Slider(start=0, end=1, step=0.05,
value=self.f_land,
title='Land Fraction')
land_albedo_slider = Slider(start=0, end=1, step=0.05,
value=self.A_land,
title='Land Albedo')
tau_star_opts = [('Mars', '0.125'),
('Earth (100 ppm CO2)', '0.66'),
('Earth (200 ppm CO2)', '0.75'),
('Earth (400 ppm CO2)', '0.84'),
('Earth (800 ppm CO2)', '0.93'),
('Earth (1600 ppm CO2)', '1.02'),
('Earth (3200 ppm CO2)', '1.12'),
('Titan', '3'),
('Venus', '125')]
greenhouse_dropdown = Dropdown(label='Preset Greenhouse Effect',
button_type='primary',
menu=tau_star_opts)
tau_star_slider = Slider(start=-1, end=np.log10(150), step=0.1,
value=self.tau_star,
title='Atmosphere Greenhouse Effect (10^x)')
refresh_s0_button = Button(label='Refresh Solar In & Calculate '
'Hab. Zone')
def _land_alb_handler(attr, old, new):
self.A_land = new
self.alpha = self.calc_albedo()
self._update_albedo_line()
def _land_frac_handler(attr, old, new):
self.f_land = new
self.alpha = self.calc_albedo()
self._update_albedo_line()
def _cloud_alb_handler(attr, old, new):
self.A_cloud = new
self.alpha = self.calc_albedo()
self._update_albedo_line()
def _cloud_frac_handler(attr, old, new):
self.f_cloud = new
self.alpha = self.calc_albedo()
self._update_albedo_line()
def _tau_slider_handler(attr, old, new):
self.tau_star = 10**new
self._update_greenhouse_line()
def _refresh_s0_handler():
refresh_s0_button.disabled = True
self._update_Ts_plot()
refresh_s0_button.disabled = False
def _tau_dropdown_handler(attr, old, new):
slide_value = np.log10(float(new))
tau_star_slider.value = slide_value
_tau_slider_handler(None, None, slide_value)
cloud_albedo_slider.on_change('value', _cloud_alb_handler)
cloud_frac_slider.on_change('value', _cloud_frac_handler)
land_albedo_slider.on_change('value', _land_alb_handler)
land_frac_slider.on_change('value', _land_frac_handler)
tau_star_slider.on_change('value', _tau_slider_handler)
refresh_s0_button.on_click(_refresh_s0_handler)
greenhouse_dropdown.on_change('value', _tau_dropdown_handler)
albedo_wx = WidgetBox(land_albedo_slider, land_frac_slider,
cloud_albedo_slider, cloud_frac_slider)
tau_wx = WidgetBox(greenhouse_dropdown, tau_star_slider,
refresh_s0_button)
return [albedo_wx, tau_wx]
def calc_Ts(self, tau, alpha):
numer = (1-alpha) * self.S0 * (1 + 0.75 * tau)
denom = 4 * self.SIGMA
return (numer / denom)**(1/4)
def calc_Ts_F(self, tau, alpha):
res = 9 / 5 * (self.calc_Ts(tau, alpha) - 273) + 32
if isinstance(res, np.ndarray):
res = res.astype(np.float32)
return res
def calc_albedo(self):
cloud = self.f_cloud * self.A_cloud
land = (1 - self.f_cloud) * self.f_land * self.A_land
alpha = cloud + land
return alpha
def _plot_Ts_grid(self):
rdylbu = bpal.RdYlBu[11]
cmapper = LinearColorMapper(palette=rdylbu, low=32, high=112)
self.img = self.plot.image([self.Ts], [0], [0.1], [1], [150],
color_mapper=cmapper)
self.img.level = 'underlay'
self.plot.xaxis.axis_label = 'Albedo'
self.plot.yaxis.axis_label = 'Greenhouse effect'
title_text = ('Surface Temp. for solar input of {:.2f} W/m^2'
''.format(self.S0))
self.plot.title.text = title_text
color_bar = ColorBar(color_mapper=cmapper, major_label_text_font_size="12pt",
label_standoff=6, location=(0, 0))
self.plot.add_layout(color_bar, 'right')
def _update_albedo_line(self):
self.alpha_line.data_source.data['x'] = [self.alpha, self.alpha]
self.terra_data.data.update(dict(alpha=[self.alpha]))
self._update_terra_div()
def _update_greenhouse_line(self):
self.tau_line.data_source.data['y'] = [self.tau_star, self.tau_star]
self.terra_data.data.update(dict(ghg_coeff=[self.tau_star]))
self._update_terra_div()
def _update_terra_div(self):
planet_Ts_F = self.calc_Ts_F(self.tau_star, self.alpha)
if 32 < planet_Ts_F < 112:
hab = 'potentially habitable'
else:
hab = 'not habitable'
div_text = ("<p style={title_style}>Terra Surface Temperature: {sfc_t:3.1f} F"
" ({habitability})</p>".format(title_style=title_style,
sfc_t=planet_Ts_F,
habitability=hab))
self.terra_div.text = div_text
def _update_Ts_plot(self):
self.S0 = self._terra_sol.get_planet_energy_in()
self.Ts = self.calc_Ts_F(self.tau_grid, self.alpha_grid)
self.img.data_source.data['image'] = [self.Ts]
self._update_terra_div()
title_text = ('Surface Temp. for solar input of {:.2f} W/m^2'
''.format(self.S0))
self.plot.title.text = title_text