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 birner(pFull, TFull, lapseC=2.0*units("K/km"), height=False):
"""
Implements the calculation of the thermal tropopause as described by Birner in
Appendix A of:
T. Birner. Fine-scale structure of the extratropical tropopause region.
Journal
"""
# Calculate the heights of the pressure levels using the hypsometric equation
z = np.zeros_like(pFull)*units.km
for h in range(0,pFull.size):
z[h] = thickness_hydrostatic(pFull[0:h+1],TFull[0:h+1])
# Calculate the lapse rate through use of a centered difference
# This needs the heights "z" at each pressure level, which can be calculated
# using the hypsometric equation, or sent as a function argument
lapse = (TFull[2:]-TFull[:-2])/(z[2:]-z[:-2])
found = False
for i in range(3,lapse.size):
if lapse[i] >= lapseC:
k = i
for j in range(k,lapse.size-2):
meanAbove = np.mean(lapse[j:j+2])
meanBelow = np.mean(lapse[j-3:j-1])
if meanAbove >= lapseC and meanBelow < lapseC:
if meanAbove > 0:
minTempIdx = np.argmin(lapse[j-3:j+2])
iTrop = k+minTempIdx
zTrop = z[iTrop]
TTrop = TFull[iTrop]
else:
print("linearly interpolated...")
minTempIdx = np.argmin(lapse[j-3:j+2])
iTrop = k+minTempIdx
# Linearly interpolate and find intersection point
ma = (TFull[j+2]-TFull[j])/(z[j+2]-z[j])
mb = (TFull[j-1]-TFull[j-3])/(z[j-1]-z[j-3])
zTrop = (TFull[j]-TFull[j-1]+mb*z[j-1]-ma*z[j])/(mb-ma)
TTrop = ma*(zTrop-z[j])+T[j]
# Find index of "layer" that has calculated tropopause
n = 0
while z[n] < zTrop:
iTrop = n
found = np.abs(zTrop-z[j]) <= 250*units.meters
found = found and pFull[iTrop] < 500*units.mbar
i2km = iTrop+1
while z[i2km] - z[iTrop] < 2000*units.meters:
found = found and (TFull[i2km]-TTrop)/(z[i2km]-zTrop) > lapseC
found = found and (TFull[i2km+1]-TTrop)/(z[i2km+1]-zTrop) > lapseC
i2km += 1
if found:
break
if found:
break
if height:
return zTrop.to(units.km)
pTrop = pFull[iTrop]
return pTrop.to(units.mbar)
def test_thickness_hydrostatic():
"""Test the thickness calculation for a moist layer."""
pressure = np.array([959., 779.2, 751.3, 724.3, 700., 269.]) * units.hPa
temperature = np.array([22.2, 14.6, 12., 9.4, 7., -38.]) * units.degC
mixing = np.array([0.01458, 0.00209, 0.00224, 0.00240, 0.00256, 0.00010])
thickness = thickness_hydrostatic(pressure, temperature, mixing=mixing)
assert_almost_equal(thickness, 9892.07 * units.m, 2)
def test_thickness_hydrostatic_isothermal_subset():
"""Test the thickness calculation for a dry isothermal layer subset at 0 degC."""
pressure = np.arange(1000, 500 - 1e-10, -10) * units.hPa
temperature = np.zeros_like(pressure) * units.degC
thickness = thickness_hydrostatic(pressure, temperature, bottom=850 * units.hPa,
depth=350 * units.hPa)
assert_almost_equal(thickness, 4242.68 * units.m, 2)
def vertical_wind_shear(u, v):
diff_u = xr.zeros_like(u[:, 1:])
diff_u.attrs[
'long_name'] = 'Horizontal wind U component delta to level below'
diff_v = xr.zeros_like(v[:, 1:])
diff_v.attrs[
'long_name'] = 'Horizontal wind V component delta to level below'
diff_u[:, :] = u[:, 1:].values - u[:, :-1].values
diff_v[:, :] = v[:, 1:].values - v[:, :-1].values
# mpcalc.bulk_shear(ls.lev[1:3].values*units.hPa, ls.u[:1, 1:3].squeeze().values*units('m/s'),
# ls.v[:1, 1:3].squeeze().values*units('m/s'), depth=25.*units.hPa)
velo_change = np.sqrt(diff_u**2 + diff_v**2)
# change of velocity is [m/s], but I want it per meter, which is dwind_dz => [m/s/m] = [1/s]
thickness = delta_height(ls.lev[1:], ls.T[:, 1:])
thickness_my = thickness.copy(deep=True)
thickness_metpy = thickness.copy(deep=True)
thickness_metpy[:, :] = 0
for i in range(len(thickness.lev)):
thickness_metpy[:, i] = mpcalc.thickness_hydrostatic(
ls.lev[i + 1:i + 3], ls.T[:1, i + 1:i + 3])[0]
shear = velo_change #/ thickness_metpy
shear.attrs['long_name'] = 'Vertical wind shear'
shear.attrs['units'] = 'm/s'
return xr.merge([ls, xr.Dataset({'dwind_dz': shear})])
def test_thickness_hydrostatic_isothermal_subset():
"""Test the thickness calculation for a dry isothermal layer subset at 0 degC."""
pressure = np.arange(1000, 500 - 1e-10, -10) * units.hPa
temperature = np.zeros_like(pressure) * units.degC
thickness = thickness_hydrostatic(pressure, temperature, bottom=850 * units.hPa,
depth=350 * units.hPa)
assert_almost_equal(thickness, 4242.68 * units.m, 2)
def test_thickness_hydrostatic():
"""Test the thickness calculation for a moist layer."""
pressure = np.array([959., 779.2, 751.3, 724.3, 700., 269.]) * units.hPa
temperature = np.array([22.2, 14.6, 12., 9.4, 7., -38.]) * units.degC
mixing = np.array([0.01458, 0.00209, 0.00224, 0.00240, 0.00256, 0.00010])
thickness = thickness_hydrostatic(pressure, temperature, mixing=mixing)
assert_almost_equal(thickness, 9892.07 * units.m, 2)
def test_thickness_hydrostatic_subset():
"""Test the thickness calculation with a subset of the moist layer."""
pressure = np.array([959., 779.2, 751.3, 724.3, 700., 269.]) * units.hPa
temperature = np.array([22.2, 14.6, 12., 9.4, 7., -38.]) * units.degC
mixing = np.array([0.01458, 0.00209, 0.00224, 0.00240, 0.00256, 0.00010])
thickness = thickness_hydrostatic(pressure, temperature, mixing=mixing,
bottom=850 * units.hPa, depth=150 * units.hPa)
assert_almost_equal(thickness, 1630.81 * units.m, 2)
def test_thickness_hydrostatic_subset():
"""Test the thickness calculation with a subset of the moist layer."""
pressure = np.array([959., 779.2, 751.3, 724.3, 700., 269.]) * units.hPa
temperature = np.array([22.2, 14.6, 12., 9.4, 7., -38.]) * units.degC
mixing = np.array([0.01458, 0.00209, 0.00224, 0.00240, 0.00256, 0.00010])
thickness = thickness_hydrostatic(pressure, temperature, mixing=mixing,
bottom=850 * units.hPa, depth=150 * units.hPa)
assert_almost_equal(thickness, 1630.81 * units.m, 2)
def coldestPoint(pFull, TFull, lapseC=2.0 * units("K/km"), height=False):
"""
Finds the tropopause as the coldest point in a sounding
"""
iTrop = np.argmin(TFull)
if height:
z = thickness_hydrostatic(pFull[0:iTrop], TFull[0:iTrop])
return z.to(units.km)
pTrop = pFull[iTrop]
return pTrop.to(units.mbar)
def moist_adiabat(z, SST):
p = 1000 * np.exp(-9.81 * z / (287. * 270.)) * units.hPa
Tp = mpcalc.moist_lapse(p, (SST - 1) * units.K)
qp = 0.8 * mpcalc.saturation_mixing_ratio(p, Tp)
ztrop1 = 17e3
ztrop2 = 19e3
idx1 = np.argmin((z - ztrop1)**2)
idx2 = np.argmin((z - ztrop2)**2)
Tp[idx1:idx2] = Tp[idx1]
Tp[idx2:] = Tp[idx1] + 2e-3 * (z[idx2:] - ztrop2) * units.K
thetap = mpcalc.potential_temperature(p, Tp)
thicknesses = [
mpcalc.thickness_hydrostatic(p, Tp, bottom=p[i], depth=p[i] - p[i + 1])
/ units.m for i in range(len(p) - 1)
]
zp = np.concatenate([[0.], np.cumsum(thicknesses)])
thetaz = np.interp(z, zp, (thetap / units.K))
qz = np.interp(z, zp, qp)
idxs = z < 35000
return z[idxs], np.array([float(x) for x in thetaz
])[idxs], np.array([float(x) for x in qz])[idxs]
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_thickness_hydrostatic_isothermal():
"""Test the thickness calculation for a dry isothermal layer at 0 degC."""
pressure = np.arange(1000, 500 - 1e-10, -10) * units.hPa
temperature = np.zeros_like(pressure) * units.degC
thickness = thickness_hydrostatic(pressure, temperature)
assert_almost_equal(thickness, 5542.12 * units.m, 2)
def wmo(pFull, TFull, lapseC=2.0 * units("K/km"), height=False):
"""
Implements NCAR's Fortran code in python:
https://github.com/NCAR/ncl/blob/develop/ni/src/lib/nfpfort/stattrop_dp.f
"""
nLev = pFull.size
nLevm = nLev - 1
pMin = 85.0 * units.mbar
pMax = 450.0 * units.mbar
dZ = 2000.0 * units.meters
g = earth_gravity
R = dry_air_gas_constant
const = g / R
found = False
lapse = np.zeros(nLevm) * units.kelvin / units.km
pHalf = np.zeros(nLevm) * units.mbar
pTrop = 0 * units.mbar
for iLev in range(0, nLevm):
lapse[iLev] = const * np.log(TFull[iLev] / TFull[iLev + 1]) / np.log(
pFull[iLev] / pFull[iLev + 1])
pHalf[iLev] = (pFull[iLev] + pFull[iLev + 1]) * 0.5
for iLev in range(0, nLevm - 1):
if lapse[iLev] < lapseC and pFull[iLev] < pMax and not found:
P1 = np.log(pHalf[iLev].magnitude)
P2 = np.log(pHalf[iLev + 1].magnitude)
if (lapse[iLev] != lapse[iLev + 1]):
weight = (lapseC - lapse[iLev]) / (lapse[iLev + 1] -
lapse[iLev])
#tropopause pressure
pTrop = np.exp(P1 + weight * (P2 - P1)) * units.mbar
else:
pTrop = pHalf[iLev]
p2km = pTrop * np.exp(-dZ * const / TFull[iLev])
lapseAvg = 0
lapseSum = 0
kount = 0
for L in range(iLev, nLevm):
if pHalf[L] > p2km:
lapseAvg = lapseSum + lapse[L]
kount = kount + 1
lapseAvg = lapseSum / kount
found = lapseAvg < lapseC
if not found:
print("Tropopause not found")
else:
iTrop = iLev
pTrop = pMin if pTrop < pMin else pTrop
if height:
z = thickness_hydrostatic(pFull[0:iTrop], TFull[0:iTrop])
return z.to(units.km)
return pTrop.to(units.mbar)
def test_thickness_hydrostatic_isothermal():
"""Test the thickness calculation for a dry isothermal layer at 0 degC."""
pressure = np.arange(1000, 500 - 1e-10, -10) * units.hPa
temperature = np.zeros_like(pressure) * units.degC
thickness = thickness_hydrostatic(pressure, temperature)
assert_almost_equal(thickness, 5542.12 * units.m, 2)
def entropy_plots(pressure,
temperature,
mixing_ratio,
altitude,
h0_std=2000,
ensemble_size=20,
ent_rate=np.arange(0, 2, 0.05),
entrain=False):
"""
plotting the summarized entropy 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.
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 entropy [joule/(kg*K)]
# sd : specific entropy of dry air
# sm1 : specific entropy of airborne mositure in state 1 (water vapor)
# sm2 : specific entropy of airborne mositure in state 2 (saturated water vapor)
sd = entropy(T.magnitude, q.magnitude * 1e-6, p.magnitude)
sm1 = entropy(T.magnitude, q.magnitude, p.magnitude)
sm2 = entropy(T.magnitude, qs.magnitude, p.magnitude)
###############################
# Water vapor calculations
p_PWtop = min(p)
#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(sd, p, '-k', linewidth=2)
ax.plot(sm1, p, '-b', linewidth=2)
ax.plot(sm2, p, '-r', linewidth=2)
# mse based on different percentages of relative humidity
qr = np.zeros((9, np.size(qs))) * units('kilogram/kilogram')
sm1_r = qr # container
for i in range(9):
qr[i, :] = qs * 0.1 * (i + 1)
sm1_r[i, :] = entropy(T.magnitude, qr[i, :].magnitude, p.magnitude)
for i in range(9):
ax.plot(sm1_r[i, :], p[:], '-', color='grey', linewidth=0.7)
ax.text(sm1_r[i, 3].magnitude - 2, 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
sm1_p = np.squeeze(np.ones((1, np.size(T))) * sm1[0])
# 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(sm1_p, p, color='green', linewidth=2)
#ax.fill_betweenx(p[lcl_idx:el_idx+1],sm1_p[lcl_idx:el_idx+1],sm2[lcl_idx:el_idx+1],interpolate=True
# ,color='green',alpha='0.3')
ax.fill_betweenx(p, sd, sm1, color='deepskyblue', alpha='0.5')
ax.set_xlabel('Specific entropies: sd, sm, sm_sat [J K$^{-1}$ kg$^{-1}$]',
fontsize=14)
ax.set_ylabel('Pressure [hPa]', fontsize=14)
ax.set_xticks([0, 50, 100, 150, 200, 250, 300, 350])
ax.set_xlim([0, 440])
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
h0offsets = np.sort(np.random.normal(
0, h0_std, ensemble_size)) * units('joule/kilogram')
# Distribution of entrainment rates
entrainment_rates = ent_rate / (units('km'))
for h0offset in h0offsets:
h4ent = sm1.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
if eps.magnitude == 0.0:
hent = np.ones(len(h4ent)) * h4ent[0] # no mixing
else:
hent = np.cumsum(dM * h4ent) / np.cumsum(dM)
# Boolean for positive buoyancy, and its topmost altitude (index) where curve is clippes
posboy = (hent > sm2)
posboy[0] = True # so there is always a detrainment level
# defining the first EL by posboy as the detrainment layer, swiching from positive buoyancy to
# negative buoyancy (0 to 1) and skipping the surface
ELindex_ent = 0
for idx in range(len(posboy) - 1):
if posboy[idx + 1] == 0 and posboy[idx] == 1 and idx > 0:
ELindex_ent = idx
break
# Plot the curve
plt.plot(hent[0:ELindex_ent + 2],
p[0:ELindex_ent + 2],
linewidth=0.6,
color='g')
#plt.plot( hent[0:], p[0:], linewidth=0.6, 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, 100])
ax2.set_xticks([0, 20, 40, 60, 80, 100])
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) * sm1[0], (1, 0) * (p[0]), color='g', linewidth=2)
# Replot the sounding on top of all that mess
ax.plot(sm2, p, color='r', linewidth=1.5)
ax.plot(sm1, p, color='b', linewidth=1.5)
# label LCL and LCF
ax.plot((sm2[lcl_idx] + (-2000, 2000) * units('joule/kilogram')),
lcl_pressure + (0, 0) * units('mbar'),
color='orange',
linewidth=3)
ax.plot((sm2[lfc_idx] + (-2000, 2000) * units('joule/kilogram')),
lfc_pressure + (0, 0) * units('mbar'),
color='magenta',
linewidth=3)
# Plot a crude histogram of parcel detrainment levels
# Text parts
ax.text(30, pressure[3], 'RH (%)', fontsize=11, color='k')
ax.text(20,
200,
'CAPE = ' + str(np.around(CAPE.magnitude, decimals=2)) + ' [J/kg]',
fontsize=12,
color='green')
ax.text(20,
250,
'CIN = ' + str(np.around(CIN.magnitude, decimals=2)) + ' [J/kg]',
fontsize=12,
color='green')
ax.text(20,
300,
'LCL = ' + str(np.around(lcl_pressure.magnitude, decimals=2)) +
' [hpa]',
fontsize=12,
color='darkorange')
ax.text(20,
350,
'LFC = ' + str(np.around(lfc_pressure.magnitude, decimals=2)) +
' [hpa]',
fontsize=12,
color='magenta')
ax.text(20,
400,
'CWV = ' + str(np.around(cwv.magnitude, decimals=2)) + ' [mm]',
fontsize=12,
color='deepskyblue')
ax.text(20,
450,
'CRH = ' + str(np.around(crh.magnitude, decimals=2)) + ' [%]',
fontsize=12,
color='blue')
ax.legend(['DEnt', 'MEnt', 'SMEnt'], fontsize=12, loc=1)
ax.set_zorder(3)
return (ax)
