def add_curves(ax,
pressure,
temperature,
mixing_ratio,
altitude,
linewidth=1.0,
LH_Tdepend=False):
"""
overlaying new curves of multiple soundings from profiles
"""
p = pressure * units('mbar')
T = temperature * units('degC')
q = mixing_ratio * units('kilogram/kilogram')
qs = mpcalc.mixing_ratio(mpcalc.saturation_vapor_pressure(T), p)
Td = mpcalc.dewpoint(mpcalc.vapor_pressure(p, q)) # dewpoint
Tp = mpcalc.parcel_profile(p, T[0], Td[0]).to('degC') # parcel profile
# Altitude based on the hydrostatic eq.
if len(altitude) == len(pressure): # (1) altitudes for whole levels
altitude = altitude * units('meter')
elif len(altitude
) == 1: # (2) known altitude where the soundings was launched
z_surf = altitude.copy() * units('meter')
# given altitude
altitude = np.zeros((np.size(T))) * units('meter')
for i in range(np.size(T)):
altitude[i] = mpcalc.thickness_hydrostatic(
p[:i + 1], T[:i + 1]) + z_surf # Hypsometric Eq. for height
else:
print(
'***NOTE***: the altitude at the surface is assumed 0 meter, and altitudes are derived based on the hypsometric equation'
)
altitude = np.zeros(
(np.size(T))) * units('meter') # surface is 0 meter
for i in range(np.size(T)):
altitude[i] = mpcalc.thickness_hydrostatic(
p[:i + 1], T[:i + 1]) # Hypsometric Eq. for height
# specific energies
if LH_Tdepend == False:
mse = mpcalc.moist_static_energy(altitude, T, q)
mse_s = mpcalc.moist_static_energy(altitude, T, qs)
dse = mpcalc.dry_static_energy(altitude, T)
else:
# A short course in cloud physics, Roger and Yau (1989)
Lvt = (2500.8 - 2.36 * T.magnitude +
0.0016 * T.magnitude**2 - 0.00006 * T.magnitude**3) * units(
'joule/gram') # latent heat of evaporation
#Lf = 2834.1 - 0.29*T - 0.004*T**2 # latent heat of fusion
mse = Cp_d * T + g * altitude + Lvt * q
mse_s = Cp_d * T + g * altitude + Lvt * qs
dse = mpcalc.dry_static_energy(altitude, T)
ax.plot(dse, p, '--k', linewidth=linewidth)
ax.plot(mse, p, '--b', linewidth=linewidth)
ax.plot(mse_s, p, '--r', linewidth=linewidth)
def add_curves_Wyoming(ax, datetime, station, linewidth=1.0, LH_Tdepend=False):
"""
overlaying new curves of multiple soundings from Wyoming datasets
date: using datetime module. ex. datetime(2018,06,06)
station: station name. ex. 'MFL' Miami, Florida
"""
from siphon.simplewebservice.wyoming import WyomingUpperAir
date = datetime
station = station
df = WyomingUpperAir.request_data(date, station)
pressure = df['pressure'].values
Temp = df['temperature'].values
Temp_dew = df['dewpoint'].values
altitude = df['height'].values
q = mpcalc.mixing_ratio(
mpcalc.saturation_vapor_pressure(Temp_dew * units('degC')),
pressure * units('mbar'))
q = mpcalc.specific_humidity_from_mixing_ratio(q)
qs = mpcalc.mixing_ratio(
mpcalc.saturation_vapor_pressure(Temp * units('degC')),
pressure * units('mbar'))
# specific energies
if LH_Tdepend == False:
mse = mpcalc.moist_static_energy(altitude * units('meter'),
Temp * units('degC'), q)
mse_s = mpcalc.moist_static_energy(altitude * units('meter'),
Temp * units('degC'), qs)
dse = mpcalc.dry_static_energy(altitude * units('meter'),
Temp * units('degC'))
else:
# A short course in cloud physics, Roger and Yau (1989)
Lvt = (2500.8 - 2.36 * T.magnitude +
0.0016 * T.magnitude**2 - 0.00006 * T.magnitude**3) * units(
'joule/gram') # latent heat of evaporation
#Lf = 2834.1 - 0.29*T - 0.004*T**2 # latent heat of fusion
mse = Cp_d * T + g * altitude + Lvt * q
mse_s = Cp_d * T + g * altitude + Lvt * qs
dse = mpcalc.dry_static_energy(altitude, T)
# adding curves on the main axes
ax.plot(dse.magnitude, pressure, 'k', linewidth=linewidth)
ax.plot(mse.magnitude, pressure, 'b', linewidth=linewidth)
ax.plot(mse_s.magnitude, pressure, 'r', linewidth=linewidth)
def msed_plots(pressure,
temperature,
mixing_ratio,
h0_std=2000,
ensemble_size=20,
ent_rate=np.arange(0, 2, 0.05),
entrain=False):
"""
plotting the summarized static energy diagram with annotations and thermodynamic parameters
"""
p = pressure * units('mbar')
T = temperature * units('degC')
q = mixing_ratio * units('kilogram/kilogram')
qs = mpcalc.mixing_ratio(mpcalc.saturation_vapor_pressure(T), p)
Td = mpcalc.dewpoint(mpcalc.vapor_pressure(p, q)) # dewpoint
Tp = mpcalc.parcel_profile(p, T[0], Td[0]).to('degC') # parcel profile
# Altitude based on the hydrostatic eq.
altitude = np.zeros((np.size(T))) * units('meter') # surface is 0 meter
for i in range(np.size(T)):
altitude[i] = mpcalc.thickness_hydrostatic(
p[:i + 1], T[:i + 1]) # Hypsometric Eq. for height
# Static energy calculations
mse = mpcalc.moist_static_energy(altitude, T, q)
mse_s = mpcalc.moist_static_energy(altitude, T, qs)
dse = mpcalc.dry_static_energy(altitude, T)
# Water vapor calculations
p_PWtop = max(200 * units.mbar,
min(p) + 1 * units.mbar) # integrating until 200mb
cwv = mpcalc.precipitable_water(Td, p,
top=p_PWtop) # column water vapor [mm]
cwvs = mpcalc.precipitable_water(
T, p, top=p_PWtop) # saturated column water vapor [mm]
crh = (cwv / cwvs) * 100. # column relative humidity [%]
#================================================
# plotting MSE vertical profiles
fig = plt.figure(figsize=[12, 8])
ax = fig.add_axes([0.1, 0.1, 0.6, 0.8])
ax.plot(dse, p, '-k', linewidth=2)
ax.plot(mse, p, '-b', linewidth=2)
ax.plot(mse_s, p, '-r', linewidth=2)
# mse based on different percentages of relative humidity
qr = np.zeros((9, np.size(qs))) * units('kilogram/kilogram')
mse_r = qr * units('joule/kilogram') # container
for i in range(9):
qr[i, :] = qs * 0.1 * (i + 1)
mse_r[i, :] = mpcalc.moist_static_energy(altitude, T, qr[i, :])
for i in range(9):
ax.plot(mse_r[i, :], p[:], '-', color='grey', linewidth=0.7)
ax.text(mse_r[i, 3].magnitude / 1000 - 1, p[3].magnitude,
str((i + 1) * 10))
# drawing LCL and LFC levels
[lcl_pressure, lcl_temperature] = mpcalc.lcl(p[0], T[0], Td[0])
lcl_idx = np.argmin(np.abs(p.magnitude - lcl_pressure.magnitude))
[lfc_pressure, lfc_temperature] = mpcalc.lfc(p, T, Td)
lfc_idx = np.argmin(np.abs(p.magnitude - lfc_pressure.magnitude))
# conserved mse of air parcel arising from 1000 hpa
mse_p = np.squeeze(np.ones((1, np.size(T))) * mse[0].magnitude)
# illustration of CAPE
el_pressure, el_temperature = mpcalc.el(p, T, Td) # equilibrium level
el_idx = np.argmin(np.abs(p.magnitude - el_pressure.magnitude))
ELps = [el_pressure.magnitude
] # Initialize an array of EL pressures for detrainment profile
[CAPE, CIN] = mpcalc.cape_cin(p[:el_idx], T[:el_idx], Td[:el_idx],
Tp[:el_idx])
plt.plot(mse_p, p, color='green', linewidth=2)
ax.fill_betweenx(p[lcl_idx:el_idx + 1],
mse_p[lcl_idx:el_idx + 1],
mse_s[lcl_idx:el_idx + 1],
interpolate=True,
color='green',
alpha='0.3')
ax.fill_betweenx(p, dse, mse, color='deepskyblue', alpha='0.5')
ax.set_xlabel('Specific static energies: s, h, hs [kJ kg$^{-1}$]',
fontsize=14)
ax.set_ylabel('Pressure [hpa]', fontsize=14)
ax.set_xticks([280, 300, 320, 340, 360, 380])
ax.set_xlim([280, 390])
ax.set_ylim(1030, 120)
if entrain is True:
# Depict Entraining parcels
# Parcel mass solves dM/dz = eps*M, solution is M = exp(eps*Z)
# M=1 at ground without loss of generality
# Distribution of surface parcel h offsets
H0STDEV = h0_std # J/kg
h0offsets = np.sort(np.random.normal(
0, H0STDEV, ensemble_size)) * units('joule/kilogram')
# Distribution of entrainment rates
entrainment_rates = ent_rate / (units('km'))
for h0offset in h0offsets:
h4ent = mse.copy()
h4ent[0] += h0offset
for eps in entrainment_rates:
M = np.exp(eps * (altitude - altitude[0])).to('dimensionless')
# dM is the mass contribution at each level, with 1 at the origin level.
M[0] = 0
dM = np.gradient(M)
# parcel mass is a sum of all the dM's at each level
# conserved linearly-mixed variables like h are weighted averages
hent = np.cumsum(dM * h4ent) / np.cumsum(dM)
# Boolean for positive buoyancy, and its topmost altitude (index) where curve is clippes
posboy = (hent > mse_s)
posboy[0] = True # so there is always a detrainment level
ELindex_ent = np.max(np.where(posboy))
# Plot the curve
plt.plot(hent[0:ELindex_ent + 2],
p[0:ELindex_ent + 2],
linewidth=0.25,
color='g')
# Keep a list for a histogram plot (detrainment profile)
if p[ELindex_ent].magnitude < lfc_pressure.magnitude: # buoyant parcels only
ELps.append(p[ELindex_ent].magnitude)
# Plot a crude histogram of parcel detrainment levels
NBINS = 20
pbins = np.linspace(1000, 150,
num=NBINS) # pbins for detrainment levels
hist = np.zeros((len(pbins) - 1))
for x in ELps:
for i in range(len(pbins) - 1):
if (x < pbins[i]) & (x >= pbins[i + 1]):
hist[i] += 1
break
det_per = hist / sum(hist) * 100
# percentages of detrainment ensumbles at levels
ax2 = fig.add_axes([0.705, 0.1, 0.1, 0.8], facecolor=None)
ax2.barh(pbins[1:],
det_per,
color='lightgrey',
edgecolor='k',
height=15 * (20 / NBINS))
ax2.set_xlim([0, max(det_per)])
ax2.set_ylim([1030, 120])
ax2.set_xlabel('Detrainment [%]')
ax2.grid()
ax2.set_zorder(2)
ax.plot([400, 400], [1100, 0])
ax.annotate('Detrainment', xy=(362, 320), color='dimgrey')
ax.annotate('ensemble: ' + str(ensemble_size * len(entrainment_rates)),
xy=(364, 340),
color='dimgrey')
ax.annotate('Detrainment', xy=(362, 380), color='dimgrey')
ax.annotate(' scale: 0 - 2 km', xy=(365, 400), color='dimgrey')
# Overplots on the mess: undilute parcel and CAPE, etc.
ax.plot((1, 1) * mse[0], (1, 0) * (p[0]), color='g', linewidth=2)
# Replot the sounding on top of all that mess
ax.plot(mse_s, p, color='r', linewidth=1.5)
ax.plot(mse, p, color='b', linewidth=1.5)
# label LCL and LCF
ax.plot((mse_s[lcl_idx] + (-2000, 2000) * units('joule/kilogram')),
lcl_pressure + (0, 0) * units('mbar'),
color='orange',
linewidth=3)
ax.plot((mse_s[lfc_idx] + (-2000, 2000) * units('joule/kilogram')),
lfc_pressure + (0, 0) * units('mbar'),
color='magenta',
linewidth=3)
### Internal waves (100m adiabatic displacements, assumed adiabatic: conserves s, sv, h).
#dZ = 100 *mpunits.units.meter
dp = 1000 * units.pascal
# depict displacements at sounding levels nearest these target levels
targetlevels = [900, 800, 700, 600, 500, 400, 300, 200] * units.hPa
for ilev in targetlevels:
idx = np.argmin(np.abs(p - ilev))
# dp: hydrostatic
rho = (p[idx]) / Rd / (T[idx])
dZ = -dp / rho / g
# dT: Dry lapse rate dT/dz_dry is -g/Cp
dT = (-g / Cp_d * dZ).to('kelvin')
Tdisp = T[idx].to('kelvin') + dT
# dhsat
dqs = mpcalc.mixing_ratio(mpcalc.saturation_vapor_pressure(Tdisp),
p[idx] + dp) - qs[idx]
dhs = g * dZ + Cp_d * dT + Lv * dqs
# Whiskers on the data plots
ax.plot((mse_s[idx] + dhs * (-1, 1)),
p[idx] + dp * (-1, 1),
linewidth=3,
color='r')
ax.plot((dse[idx] * (1, 1)),
p[idx] + dp * (-1, 1),
linewidth=3,
color='k')
ax.plot((mse[idx] * (1, 1)),
p[idx] + dp * (-1, 1),
linewidth=3,
color='b')
# annotation to explain it
if ilev == 400 * ilev.units:
ax.plot(360 * mse_s.units + dhs * (-1, 1) / 1000,
440 * units('mbar') + dp * (-1, 1),
linewidth=3,
color='r')
ax.annotate('+/- 10mb', xy=(362, 440), fontsize=8)
ax.annotate(' adiabatic displacement', xy=(362, 460), fontsize=8)
# Plot a crude histogram of parcel detrainment levels
# Text parts
ax.text(290, pressure[3], 'RH (%)', fontsize=11, color='k')
ax.text(285,
200,
'CAPE = ' + str(np.around(CAPE.magnitude, decimals=2)) + ' [J/kg]',
fontsize=12,
color='green')
ax.text(285,
250,
'CIN = ' + str(np.around(CIN.magnitude, decimals=2)) + ' [J/kg]',
fontsize=12,
color='green')
ax.text(285,
300,
'LCL = ' + str(np.around(lcl_pressure.magnitude, decimals=2)) +
' [hpa]',
fontsize=12,
color='darkorange')
ax.text(285,
350,
'LFC = ' + str(np.around(lfc_pressure.magnitude, decimals=2)) +
' [hpa]',
fontsize=12,
color='magenta')
ax.text(285,
400,
'CWV = ' + str(np.around(cwv.magnitude, decimals=2)) + ' [mm]',
fontsize=12,
color='deepskyblue')
ax.text(285,
450,
'CRH = ' + str(np.around(crh.magnitude, decimals=2)) + ' [%]',
fontsize=12,
color='blue')
ax.legend(['DSE', 'MSE', 'SMSE'], fontsize=12, loc=1)
ax.set_zorder(3)
return (ax)
def test_dry_static_energy():
"""Test the dry static energy calculation."""
dse = dry_static_energy(1000 * units.m, 25 * units.degC)
assert_almost_equal(dse, 309.4474 * units('kJ/kg'), 6)
def test_dry_static_energy():
"""Test the dry static energy calculation."""
dse = dry_static_energy(1000 * units.m, 25 * units.degC)
assert_almost_equal(dse, 309.4474 * units('kJ/kg'), 6)