def sigma_r(refprs, press, temp, salty):
'''Calculate density using international equation of state
From text furnished by J. Gieskes
Args:
press -- pressure in decibars
temp -- temperature in celsius degrees
salty -- salinity PSS 78
refprs -- reference pressure
refprs = 0. : sigma theta
refprs = press: sigma z
Return:
kg/m*3 - 1000.0
'''
# check for missing data
if _any_missing(temp, press, salty):
return CDMISS
# calculate potential temperature
if press != refprs:
potemp = potential_temperature(press, temp, salty, refprs)
else:
potemp = temp
# sigma theta kg/m**3
sigma = (rho_w(potemp) + kw(potemp, salty) + k_st0(salty, potemp) +
_decimal(4.8314e-4) * salty ** 2)
if equal_with_epsilon(refprs, 0.0):
return sigma - _decimal(1000.0)
# Calculate pressure effect
#
# rho(s,t,0)/(1.0-p/k(s,t,p))
#
kst0 = secant_bulk_modulus(abs(salty), potemp, 0)
# reference pressure in bars
bars = refprs * 0.1
# Calculate pressure terms
terma = polynomial(potemp, (3.239908, 0.00143713, 1.16092e-4, -5.77905e-7)) + \
polynomial(potemp, (0.0022838, -1.0981e-5, -1.6078e-6)) * salty + \
1.91075e-4 * abs(salty) ** 1.5
termb = polynomial(potemp, (8.50935e-5, -6.12293e-6, 5.2787e-8)) + \
polynomial(potemp, (-9.9348e-7, 2.0816e-8, 9.1697e-10)) * salty
# Secant bulk modulus k(s,t,p) */
kstp = polynomial(bars, (kst0, terma, termb))
return sigma / (1.0 - bars / kstp) - 1000.0
def potential_temperature(p, t, s, rp):
'''Calculate potential temperature for an arbitrary reference pressure.
Ref: N.P. Fofonoff
Deep Sea Research
in press Nov 1976
Args:
press-- pressure in decibars
temp -- temperature in celsius degrees
s -- salinity PSS 78
rp -- reference pressure in decibars
(0.0 for standard potential temperature)
Return:
potential temperature
'''
s1 = s - 35.0
if _any_missing(s, p, t):
return CDMISS
dp = rp - p
n = int(abs(dp) / 1.0e3) + 1
dp /= float(n)
for i in range(1, n):
for j in range(1, 4):
r1 = polynomial(t, (-4.6206e-13, 1.8676e-14, -2.1687e-16)) * p
r2 = polynomial(t, (-1.1351e-10, 2.7759e-12)) * s1
r3 = polynomial(t, (0, -6.7795e-10, 8.733e-12, -5.4481e-13))
r4 = (r1 + (r2 + r3 + 1.8741e-8)) * p + \
polynomial(t, (1.8932e-6, -4.2393e-8)) * s1
r5 = r4 + polynomial(
t, (3.5803e-5, 8.5258e-6, -6.836e-8, 6.6228e-10))
x = dp * r5
if j == 1:
t = t + 0.5 * x
q = x
p += 0.5 * dp
elif j == 2:
t += 0.29289322 * (x - q)
q = 0.58578644 * x + 0.121320344 * q
elif j == 3:
t += 1.707106781 * (x - q)
q = 3.414213562 * x - 4.121320344 * q
p += 0.5 * dp
elif j == 4:
t += (x - 2.0 * q) / 6.0
return t
def pressure(z):
'''Calculates pressure from depth.
Args:
z - depth
'''
if _missing(z):
return CDMISS
return polynomial(z, COEFF_PRESSURE)
def oxycal(pt, s, o2):
'''Routine to calculate precent oxygen saturation.
Args:
-> ptx potential temperature.
-> salx salinity
-> o2x observed oxygen (ml/l)
Return:
percent oxygen saturation.
Ref: Weiss, R.F. (1970) The Solubility of Nitrogen, Oxygen,
and Argon in Water and Seawater. Deep-Sea Res., Vol 17,
721-735.
Note: two other values can be calculated using returned value.
o2c == oxygen saturation of parcel of water moved
to surface and exposed to the atmosphere for
an infinite amount of time.
o2c = (o2x*100.)/oxypct
apparent oxygen utilization: o2x - o2c
'''
if _any_missing(pt, s, o2):
return CDMISS
a1 = -173.4292
a2 = 249.6339
a3 = 143.3483
a4 = -21.8492
b = (-0.033096, 0.014259, -0.0017)
pt += 273.15
ptpc = pt / 100.0
o2c = exp(a1 + a2 * (100.0 / pt) + a3 * log(ptpc) + a4 * ptpc +
s * polynomial(ptpc, b))
return (o2 / o2c) * 100.0
def k_st0(salinity, potential_temperature):
return polynomial(potential_temperature, COEFF_K_ST0) * \
abs(salinity) ** _decimal(1.5)
def kw_1(potential_temperature):
return polynomial(potential_temperature, COEFF_KW_1)
def rho_w(potential_temperature):
'''density of pure water kg/m**3'''
return polynomial(potential_temperature, COEFF_RHO_W)
def test_polynomial(self):
self.assertEqual(0, fns.polynomial(5, []))
self.assertEqual(1, fns.polynomial(5, [1]))
self.assertEqual(5, fns.polynomial(5, [0, 1]))
self.assertEqual(30, fns.polynomial(5, [0, 1, 1]))
self.assertEqual(50, fns.polynomial(5, [0, 5, 1]))