def invert_theta_l(theta_l, rt, p):
T = thermo.theta_to_T(theta_l, p)
r_star = thermo.r_star(p, T)
if r_star < rt:
T0 = numpy.array([233.15, theta_l])
T = rootfinder.fzero(Tfind, T0, p, theta_l, rt)
return T
def make_rt_vs_theta_l(tlmin, tlmax, rtmin, rtmax, p):
#make a blank skewT diagram
clf()
#get a dense range of p, t0 to contour
theta_l_vals = linspace(tlmin, tlmax, 100)
r_vals = linspace(rtmin, rtmax, 100)
theta_l_vals, r_vals = meshgrid(theta_l_vals, r_vals)
Tvals = zeros(theta_l_vals.shape, float)
for i in range(100):
for j in range(100):
Tvals[j,i] = invert_theta_l(theta_l_vals[j,i], r_vals[j,i], p)
#use the real (data) value to get the potential temperature
r_star = thermo.r_star(p, Tvals)
rl = r_vals - r_star
rl[rl < 0.] = 0.
r = r_vals - rl
theta_v = thermo.theta_v(p, Tvals, r)
contour(theta_l_vals, r_vals*1000., -theta_v, 20, colors='k', linestyles=':')
axis([tlmin, tlmax, rtmin*1000., rtmax*1000.])
title('(theta_l, rt) Conserved Variable Diagram')
ylabel('rt (g kg-1)')
xlabel('theta_l (K)')
def make_rt_vs_theta_l(tlmin, tlmax, rtmin, rtmax, p):
#make a blank skewT diagram
clf()
#get a dense range of p, t0 to contour
theta_l_vals = linspace(tlmin, tlmax, 100)
r_vals = linspace(rtmin, rtmax, 100)
theta_l_vals, r_vals = meshgrid(theta_l_vals, r_vals)
Tvals = zeros(theta_l_vals.shape, float)
for i in range(100):
for j in range(100):
Tvals[j, i] = invert_theta_l(theta_l_vals[j, i], r_vals[j, i], p)
#use the real (data) value to get the potential temperature
r_star = thermo.r_star(p, Tvals)
rl = r_vals - r_star
rl[rl < 0.] = 0.
r = r_vals - rl
theta_v = thermo.theta_v(p, Tvals, r)
contour(theta_l_vals,
r_vals * 1000.,
-theta_v,
20,
colors='k',
linestyles=':')
axis([tlmin, tlmax, rtmin * 1000., rtmax * 1000.])
title('(theta_l, rt) Conserved Variable Diagram')
ylabel('rt (g kg-1)')
xlabel('theta_l (K)')
def invert_theta_l(theta_l, rt, p):
T = thermo.theta_to_T(theta_l, p)
r_star = thermo.r_star(p, T)
if r_star < rt:
T0 = numpy.array([233.15, theta_l])
T = rootfinder.fzero(Tfind, T0, p, theta_l, rt)
return T
def _main(tmin, tmax, rmin, rmax):
result = _get_sounding('sounding.txt')
T = result['T']
p = result['p']
RH = result['RH']
rt = thermo.p_T_RH_to_r(p, T, RH)
r_star = thermo.r_star(p, T)
rl = rt - r_star
rl[rl < 0] = 0.
r = rt - rl
plot_rt_vs_theta_alpha(p, T, r, rl, 1.)
show()
def make_skewT(tmin, tmax, pmax, pmin, skew=30.):
#make a blank skewT diagram
clf()
#get a dense range of p, t0 to contour
yplot = linspace(1050, 100, 100)
xplot = linspace(-50, 50, 100)
xplot, yplot = meshgrid(xplot, yplot)
#lay down a reference grid that labels xplot,yplot points
#in the new (skewT-lnP) coordinate system .
# Each value of the temp matrix holds the actual (data) temperature
# label (in deg C) of the xplot, yplot coordinate pairs
#note that we don't have to transform the y coordinate
#it's still the pressure
#use the real (data) value to get the potential temperature
T = xplot + skew*log(0.001*yplot)
Tk = T + 273.15 #convert from C to K for use in thermo functios
p = yplot*100. #convert from hPa to Pa
th = thermo.theta(p, Tk) #theta labels
#add the mixing ratio
rstar = thermo.r_star(p, Tk) #wsat labels
#saturated adiabat, so Tdew=Tk
thetaeVals = thermo.theta_e(p, Tk, rstar, 0.)
tempLabels = arange(-140., 50., 10.)
con1 = contour(xplot, yplot, T, levels = tempLabels, colors = 'k', linewidths=.5)
ax = gca()
ax.set_yscale('log')
lines = arange(100., 1100., 100.)
yticks(lines, ['100','200','300','400','500','600','700','800','900','1000'])
for line in lines:
axhline(line, ls=':', color='k', linewidth=.5)
thetaLabels = arange(200., 380., 10.)
con2 = contour(xplot, yplot, th, levels = thetaLabels, colors='b', linewidths=.5)
#rsLabels = [.1,.2,.4,.6, 1, 2, 3, 4, 5, 6, 8, 10, 15, 20, 25, 30, 40]
#con3 = contour(xplot, yplot, rstar*1.e3, levels=rsLabels, colors='g', linewidths=.5)
#thetaeLabels = linspace(200,400,21)
#con4 = contour(xplot, yplot, thetaeVals, levels = thetaeLabels, colors='r', linewidths=.5)
axis([tmin, tmax, pmax, pmin])
clabel(con1, inline = False, fmt = '%1.0f')
clabel(con2, inline = False, fmt = '%1.0f')
#clabel(con3, inline = False, fmt = '%1.1f')
#clabel(con4, inline = False, fmt = '%1.0f')
title('skew T - lnp chart')
ylabel('pressure (hPa)')
xlabel('temperature (black, degrees C)')
def _main(tmin, tmax, rmin, rmax):
result = _get_sounding('sounding.txt')
T = result['T']
p = result['p']
RH = result['RH']
rt = thermo.p_T_RH_to_r(p, T, RH)
r_star = thermo.r_star(p, T)
rl = rt - r_star
rl[rl < 0] = 0.
r = rt - rl
plot_rt_vs_theta_alpha(p, T, r, rl, 1.)
show()
def main(tmin, tmax, rmin, rmax):
result = get_sounding('sounding.txt')
T = result['T']
p = result['p']
RH = result['RH']
rt = thermo.p_T_RH_to_r(p, T, RH)
make_rt_vs_theta_l(270, 310, 0./1000., 6./1000., 84000.)
r_star = thermo.r_star(p, T)
rl = rt - r_star
rl[rl < 0] = 0.
r = rt - rl
plot_rt_vs_theta_l(p, T, r, rl)
axis([270,310,0,6])
show()
def main(tmin, tmax, rmin, rmax):
result = get_sounding('sounding.txt')
T = result['T']
p = result['p']
RH = result['RH']
rt = thermo.p_T_RH_to_r(p, T, RH)
make_rt_vs_theta_l(270, 310, 0. / 1000., 6. / 1000., 84000.)
r_star = thermo.r_star(p, T)
rl = rt - r_star
rl[rl < 0] = 0.
r = rt - rl
plot_rt_vs_theta_l(p, T, r, rl)
axis([270, 310, 0, 6])
show()
def Tfind(Tguess, p, theta_l, rt):
# due to the check in invert_theta_l, we can assume that r = r_star.
# However, we don't know the exact value of r_star because we don't know T.
r = thermo.r_star(p, Tguess)
rl = rt - r
return theta_l - thermo.theta_l(p, Tguess, r, rl)
def make_skewT(tmin, tmax, pmax, pmin, skew=30.):
#make a blank skewT diagram
clf()
#get a dense range of p, t0 to contour
yplot = linspace(1050, 100, 100)
xplot = linspace(-50, 50, 100)
xplot, yplot = meshgrid(xplot, yplot)
#lay down a reference grid that labels xplot,yplot points
#in the new (skewT-lnP) coordinate system .
# Each value of the temp matrix holds the actual (data) temperature
# label (in deg C) of the xplot, yplot coordinate pairs
#note that we don't have to transform the y coordinate
#it's still the pressure
#use the real (data) value to get the potential temperature
T = xplot + skew * log(0.001 * yplot)
Tk = T + 273.15 #convert from C to K for use in thermo functios
p = yplot * 100. #convert from hPa to Pa
th = thermo.theta(p, Tk) #theta labels
#add the mixing ratio
rstar = thermo.r_star(p, Tk) #wsat labels
#saturated adiabat, so Tdew=Tk
thetaeVals = thermo.theta_e(p, Tk, rstar, 0.)
tempLabels = arange(-140., 50., 10.)
con1 = contour(xplot,
yplot,
T,
levels=tempLabels,
colors='k',
linewidths=.5)
ax = gca()
ax.set_yscale('log')
lines = arange(100., 1100., 100.)
yticks(lines, [
'100', '200', '300', '400', '500', '600', '700', '800', '900', '1000'
])
for line in lines:
axhline(line, ls=':', color='k', linewidth=.5)
thetaLabels = arange(200., 380., 10.)
con2 = contour(xplot,
yplot,
th,
levels=thetaLabels,
colors='b',
linewidths=.5)
rsLabels = [.1, .2, .4, .6, 1, 2, 3, 4, 5, 6, 8, 10, 15, 20, 25, 30, 40]
con3 = contour(xplot,
yplot,
rstar * 1.e3,
levels=rsLabels,
colors='g',
linewidths=.5)
thetaeLabels = linspace(200, 400, 21)
con4 = contour(xplot,
yplot,
thetaeVals,
levels=thetaeLabels,
colors='r',
linewidths=.5)
axis([tmin, tmax, pmax, pmin])
clabel(con1, inline=False, fmt='%1.0f')
clabel(con2, inline=False, fmt='%1.0f')
clabel(con3, inline=False, fmt='%1.1f')
clabel(con4, inline=False, fmt='%1.0f')
title('skew T - lnp chart')
ylabel('pressure (hPa)')
xlabel('temperature (black, degrees C)')
def Tfind(Tguess, p, theta_l, rt):
# due to the check in invert_theta_l, we can assume that r = r_star.
# However, we don't know the exact value of r_star because we don't know T.
r = thermo.r_star(p, Tguess)
rl = rt - r
return theta_l - thermo.theta_l(p, Tguess, r, rl)