def plot_cdf(cfg, psi_cube, ecs_cube, obs_cube):
"""Plot cumulative distribution function of ECS."""
confidence_level = cfg.get('confidence_level', 0.66)
(ecs_lin, ecs_pdf) = ec.gaussian_pdf(psi_cube.data, ecs_cube.data,
np.mean(obs_cube.data),
np.std(obs_cube.data))
ecs_cdf = ec.cdf(ecs_lin, ecs_pdf)
# Provenance
filename = 'cdf_{}'.format(obs_cube.attributes['dataset'])
netcdf_path = get_diagnostic_filename(filename, cfg)
cube = iris.cube.Cube(ecs_cdf,
var_name='cdf',
long_name='Cumulative distribution function',
units='1')
cube.add_aux_coord(
iris.coords.AuxCoord(ecs_lin, **ih.convert_to_iris(ECS_ATTRS)), 0)
io.iris_save(cube, netcdf_path)
project = _get_project(cfg)
provenance_record = get_provenance_record(
"The CDF for ECS. The horizontal dot-dashed lines show the {}% "
"confidence limits. The orange histograms show the prior "
"distributions that arise from equal weighting of the {} models in "
"0.5 K bins.".format(int(confidence_level * 100), project), ['mean'],
['other'], _get_ancestor_files(cfg, obs_cube.attributes['dataset']))
# Plot
if cfg['write_plots']:
AXES.plot(ecs_lin,
ecs_cdf,
color='black',
linewidth=2.0,
label='Emergent constraint')
AXES.hist(ecs_cube.data,
bins=6,
range=(2.0, 5.0),
cumulative=True,
density=True,
color='orange',
label='{} models'.format(project))
AXES.axhline((1.0 - confidence_level) / 2.0,
color='black',
linestyle='dashdot')
AXES.axhline((1.0 + confidence_level) / 2.0,
color='black',
linestyle='dashdot')
# Plot appearance
AXES.set_title('CDF of emergent constraint')
AXES.set_xlabel('ECS / K')
AXES.set_ylabel('CDF')
legend = AXES.legend(loc='upper left')
# Save plot
provenance_record['plot_file'] = _save_fig(cfg, filename, legend)
# Write provenance
with ProvenanceLogger(cfg) as provenance_logger:
provenance_logger.log(netcdf_path, provenance_record)
def plot_pdf(cfg, psi_cube, ecs_cube, obs_cube):
"""Plot probability density function of ECS."""
obs_mean = np.mean(obs_cube.data)
obs_std = np.std(obs_cube.data)
(ecs_lin, ecs_pdf) = ec.gaussian_pdf(psi_cube.data, ecs_cube.data,
obs_mean, obs_std)
# Provenance
filename = 'pdf_{}'.format(obs_cube.attributes['dataset'])
netcdf_path = get_diagnostic_filename(filename, cfg)
cube = iris.cube.Cube(ecs_pdf,
var_name='pdf',
long_name='Probability density function',
units='K-1')
cube.add_aux_coord(
iris.coords.AuxCoord(ecs_lin, **ih.convert_to_iris(ECS_ATTRS)), 0)
io.iris_save(cube, netcdf_path)
project = _get_project(cfg)
provenance_record = get_provenance_record(
"The PDF for ECS. The orange histograms show the prior distributions "
"that arise from equal weighting of the {} models in 0.5 K bins.".
format(project), ['mean'], ['other'],
_get_ancestor_files(cfg, obs_cube.attributes['dataset']))
# Plot
if cfg['write_plots']:
AXES.plot(ecs_lin,
ecs_pdf,
color='black',
linewidth=2.0,
label='Emergent constraint')
AXES.hist(ecs_cube.data,
bins=6,
range=(2.0, 5.0),
density=True,
color='orange',
label='{} models'.format(project))
# Plot appearance
AXES.set_title('PDF of emergent constraint')
AXES.set_xlabel('ECS / K')
AXES.set_ylabel('Probability density')
legend = AXES.legend(loc='upper left')
# Save plot
provenance_record['plot_file'] = _save_fig(cfg, filename, legend)
# Write provenance
with ProvenanceLogger(cfg) as provenance_logger:
provenance_logger.log(netcdf_path, provenance_record)
def get_constraint(x_data, y_data, x_ref, x_ref_err):
"""Print constraint value for Y axis."""
(feature, feature_units, label, label_units) = _get_tags(x_data, y_data)
x_data = x_data.values.squeeze()
y_data = y_data.values.squeeze()
x_ref = x_ref.values.squeeze()
x_ref_err = x_ref_err.values.squeeze()
(y_data_lin, y_pdf) = ec.gaussian_pdf(x_data, y_data, x_ref, x_ref_err**2)
y_mean = np.sum(y_data_lin * y_pdf) / np.sum(y_pdf)
y_var = np.sum((y_data_lin - y_mean)**2 * y_pdf) / np.sum(y_pdf)
y_std = np.sqrt(y_var)
lines = ec.regression_surface(x_data, y_data)
logger.info("Observational constraint on '%s': (%.3f ± %.3f) %s", feature,
x_ref, x_ref_err, feature_units)
logger.info("Constraint on target variable '%s': (%.3f ± %.3f) %s", label,
y_mean, y_std, label_units)
logger.info("R2 of emergent relationship: %.3f (p = %.4f)", lines['R2'],
lines['p'][0])
return (y_mean, y_std)
def get_ecs_range(cfg, psi_cube, ecs_cube, obs_cube):
"""Get constrained ecs range."""
confidence_level = cfg.get('confidence_level', 0.66)
conf_low = (1.0 - confidence_level) / 2.0
conf_high = (1.0 + confidence_level) / 2.0
# Calculate PDF and CDF
(ecs_lin, ecs_pdf) = ec.gaussian_pdf(psi_cube.data, ecs_cube.data,
np.mean(obs_cube.data),
np.std(obs_cube.data))
ecs_cdf = ec.cdf(ecs_lin, ecs_pdf)
# Calculate constrained ECS range
ecs_mean = ecs_lin[np.argmax(ecs_pdf)]
ecs_index_range = np.where((ecs_cdf >= conf_low)
& (ecs_cdf <= conf_high))[0]
ecs_range = ecs_lin[ecs_index_range]
ecs_low = min(ecs_range)
ecs_high = max(ecs_range)
return (ecs_mean, ecs_low, ecs_high)
def main(cfg):
"""Run the diagnostic."""
input_data = (
select_metadata(cfg['input_data'].values(), short_name='tas') +
select_metadata(cfg['input_data'].values(), short_name='tasa'))
if not input_data:
raise ValueError("This diagnostics needs 'tas' or 'tasa' variable")
# Get time-dependent data
(tas_cubes, tas_obs) = get_tas(input_data)
(psi_cubes, psi_obs) = get_psi(cfg)
# Get scalar psi, ECS and climate feedback parameter for models
(psi_cube, ecs_cube, lambda_cube) = get_external_cubes(cfg)
# Plots
for obs_name in tas_obs:
logger.info("Observation for tas: %s", obs_name)
plot_temperature_anomaly(cfg, tas_cubes, lambda_cube, obs_name)
for obs_name in psi_obs:
logger.info("Observation for psi: %s", obs_name)
plot_psi(cfg, psi_cubes, lambda_cube, obs_name)
obs_cube = psi_cubes[obs_name]
plot_emergent_relationship(cfg, psi_cube, ecs_cube, lambda_cube,
obs_cube)
(ecs_lin, ecs_pdf) = ec.gaussian_pdf(psi_cube.data, ecs_cube.data,
np.mean(obs_cube.data),
np.var(obs_cube.data))
plot_pdf(cfg, ecs_lin, ecs_pdf, ecs_cube, obs_name)
plot_cdf(cfg, ecs_lin, ecs_pdf, ecs_cube, obs_name)
# Print ECS range
ecs_range = get_ecs_range(cfg, ecs_lin, ecs_pdf)
logger.info("Observational constraint: Ψ = (%.2f ± %.2f) K",
np.mean(obs_cube.data), np.std(obs_cube.data))
logger.info(
"Constrained ECS range: (%.2f - %.2f) K with best "
"estimate %.2f K", ecs_range[1], ecs_range[2], ecs_range[0])