From 46445d34518f50610f67919e75a54f3c195682bf Mon Sep 17 00:00:00 2001
From: bjorn-stevens <64255981+bjorn-stevens@users.noreply.github.com>
Date: Sun, 14 Aug 2022 22:24:58 +0200
Subject: [PATCH] added a function to calculate (moist) static energy
in the atmospheric sciences there are many different moist static
energies. They differ due to the choice of reference enthalpies for
water phases, which are connected by the phase change enthalpies, and
thus have a single degree of freedom. This we give to the reference
enthalpy (enthalpy at T0) for vapor. The choice of hv0 matters because
not all reference quantities can be zero for all phases of water, and so
the choice influences how the reference quantity weights different water
phases.
the function has been defined in a rather expressive way to bring out
this property and make it possible to compute one or the other of the
moist static energies by choosing a different reference state for the
vapor enthalpy.
---
moist_thermodynamics/functions.py | 49 ++++++++++++++++++++++++-------
1 file changed, 39 insertions(+), 10 deletions(-)
diff --git a/moist_thermodynamics/functions.py b/moist_thermodynamics/functions.py
index 9db6cab..3c897f3 100644
--- a/moist_thermodynamics/functions.py
+++ b/moist_thermodynamics/functions.py
@@ -358,28 +358,57 @@ def saturation_partition(P, ps, qt):
return np.minimum(qt, qs)
-def static_energy(TK, qv=0.0, ql=0.0, qi=0.0):
- """Returns the static energy, defaulting to that for a dry atmosphere
-
- The moist static energy is calculated so that it includes the effects of composition
- on the specific heat if specific humidities are included, but defaults to the dry static energy
+def static_energy(T, Z, qv=0, ql=0, qi=0, hv0=constants.cpv * constants.T0):
+ """Returns the static energy
+
+ The static energy is calculated so that it includes the effects of composition on the
+ specific heat if specific humidities are included. Different common forms of the static
+ energy arise from different choices of the reference state and condensate loading:
+ - hv0 = cpv*T0 -> frozen, liquid moist static energy
+ - hv0 = ls0 + ci*T0 -> frozen moist static energy
+ - hv0 = cpv*T0 -> liquid water static energy if qi= 0 (default if qv /= 0)
+ - hv0 = lv0 + cl*T0 -> moist static energy if qi= 0.
+ - qv=ql=q0=0 -> dry static energy (default)
+
+ Because the composition weights the reference enthalpies, different choices do not differ by
+ a constant, but rather by a constant weighted by the specific masses of the different water
+ phases.
Args:
- TK: temperature in kelvin
- PPa: pressure in pascal
+ T: temperature in kelvin
+ Z: altitude (above mean sea-level) in meters
qv: specific vapor mass
ql: specific liquid mass
qi: specific ice mass
+ hv0: reference vapor enthalpy
+
+ >>> static_energy(300.,600.,15.e-3,hv0=constants.lv0 + constants.cl * constants.T0)
+ 358162.78621841426
+
"""
cpd = constants.isobaric_dry_air_specific_heat
cpv = constants.isobaric_water_vapor_specific_heat
cl = constants.liquid_water_specific_heat
ci = constants.frozen_water_specific_heat
+ lv0 = constants.lv0
+ ls0 = constants.ls0
+ T0 = constants.T0
g = constants.gravity_earth
- qt = qv + ql + qi
- cp = cpd + qt * (cl - cpd)
- return TK * cp + qv * lv + gz
+ qd = 1.0 - qv - ql - qi
+ cp = qd * cpd + qv * cpv + ql * cl + qi * ci
+
+ h = (
+ qd * cpd * T
+ + qv * cpv * T
+ + ql * cl * T
+ + qi * ci * T
+ + qv * (hv0 - cpv * T0)
+ + ql * (hv0 - lv0 - cl * T0)
+ + qi * (hv0 - ls0 - ci * T0)
+ + g * Z
+ )
+ return h
def theta(TK, PPa, qv=0.0, ql=0.0, qi=0.0):
--
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