diff --git a/.gitignore b/.gitignore
index 0d20b6487c61e7d1bde93acf4a14b7a89083a16d..4a3d2739681806a9139c374930f3a191d56341d4 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1 +1,8 @@
*.pyc
+build
+moist_thermodynamics.egg-info
+*/.ipynb_checkpoints
+.ipynb_checkpoints
+
+data/*
+moist_thermodynamics/plots/*.pdf
diff --git a/examples/saturation-water-vapor.ipynb b/examples/saturation-water-vapor.ipynb
index 2a0fd38c8de85b5a84fc2e55bad2bb2f726182bb..3db1bd2a7d1a5bd8ce75ea07acd8b5d46aa5f298 100644
--- a/examples/saturation-water-vapor.ipynb
+++ b/examples/saturation-water-vapor.ipynb
@@ -48,34 +48,35 @@
"source": [
"gravity = 9.8076\n",
"\n",
- "cpd = 1006.\n",
- "Rd = 287.05\n",
- "\n",
- "Rv = 461.53 # IAPWS97 at 273.15\n",
- "cpv = 1865.01 # ''\n",
- "lv0 = 2500.93e3 # IAPWS97 at 273.15\n",
- "lf0 = 333.42e3 #''\n",
- "\n",
- "cl = 4179.57 # IAPWS97 at 305 and P=0.1 MPa (chosen to give a good fit for es over ice)\n",
- "ci = 1905.43 # IAPWS97 at 247.065 and P=0.1 MPa (chosen to give a good fit for es over ice)\n",
- "\n",
- "eps1 = Rd/Rv\n",
- "eps2 = Rv/Rd -1.\n",
- "\n",
- "P0 = 100000. # Standard Pressure\n",
- "T0 = 273.15 # Standard Temperature\n",
- "PvC = 22.064e6 # Critical pressure of water vapor\n",
- "TvC = 647.096 # Critical temperature of water vapor\n",
- "TvT = 273.16 # Triple point temperature of water\n",
- "PvT = 611.655\n",
- "lvT = lv0 + (cpv-cl)*(TvT-T0)\n",
- "lfT = lf0 + (cpv-ci)*(TvT-T0)\n",
- "lsT = lvT + lfT\n",
- "\n",
- "es_default = 'sonntag'\n",
- "\n",
- "def thermo_input(x, xtype='none'):\n",
- " \n",
+ "cpd = 1006.0\n",
+ "Rd = 287.05\n",
+ "\n",
+ "Rv = 461.53 # IAPWS97 at 273.15\n",
+ "cpv = 1865.01 # ''\n",
+ "lv0 = 2500.93e3 # IAPWS97 at 273.15\n",
+ "lf0 = 333.42e3 #''\n",
+ "\n",
+ "cl = 4179.57 # IAPWS97 at 305 and P=0.1 MPa (chosen to give a good fit for es over ice)\n",
+ "ci = 1905.43 # IAPWS97 at 247.065 and P=0.1 MPa (chosen to give a good fit for es over ice)\n",
+ "\n",
+ "eps1 = Rd / Rv\n",
+ "eps2 = Rv / Rd - 1.0\n",
+ "\n",
+ "P0 = 100000.0 # Standard Pressure\n",
+ "T0 = 273.15 # Standard Temperature\n",
+ "PvC = 22.064e6 # Critical pressure of water vapor\n",
+ "TvC = 647.096 # Critical temperature of water vapor\n",
+ "TvT = 273.16 # Triple point temperature of water\n",
+ "PvT = 611.655\n",
+ "lvT = lv0 + (cpv - cl) * (TvT - T0)\n",
+ "lfT = lf0 + (cpv - ci) * (TvT - T0)\n",
+ "lsT = lvT + lfT\n",
+ "\n",
+ "es_default = \"sonntag\"\n",
+ "\n",
+ "\n",
+ "def thermo_input(x, xtype=\"none\"):\n",
+ "\n",
" import numpy as np\n",
"\n",
" x = np.asarray(x).flatten()\n",
@@ -84,175 +85,272 @@
" x = x[None] # Makes x 1D\n",
" scalar_input = True\n",
"\n",
- " if (xtype == 'Kelvin' and x.max() < 100 ): x = x+273.15\n",
- " if (xtype == 'Celcius'and x.max() > 100 ): x = x-273.15\n",
- " if (xtype == 'Pascal' and x.max() < 1200): x = x*100.\n",
- " if (xtype == 'kg/kg' and x.max() > 1.0) : x = x/1000.\n",
- " if (xtype == 'meter' and x.max() < 10.0): print('Warning: input should be in meters, max value less than 10, not corrected')\n",
+ " if xtype == \"Kelvin\" and x.max() < 100:\n",
+ " x = x + 273.15\n",
+ " if xtype == \"Celcius\" and x.max() > 100:\n",
+ " x = x - 273.15\n",
+ " if xtype == \"Pascal\" and x.max() < 1200:\n",
+ " x = x * 100.0\n",
+ " if xtype == \"kg/kg\" and x.max() > 1.0:\n",
+ " x = x / 1000.0\n",
+ " if xtype == \"meter\" and x.max() < 10.0:\n",
+ " print(\n",
+ " \"Warning: input should be in meters, max value less than 10, not corrected\"\n",
+ " )\n",
"\n",
" return x, scalar_input\n",
"\n",
+ "\n",
"def eslf(T, formula=es_default):\n",
- " \"\"\" Returns the saturation vapour pressure [Pa] over liquid given \n",
- "\tthe temperature. Temperatures can be in Celcius or Kelvin.\n",
- "\tFormulas supported are\n",
- "\t - Goff-Gratch (1994 Smithsonian Tables)\n",
- "\t - Sonntag (1994) \n",
- "\t - Flatau\n",
- "\t - Magnus Tetens (MT)\n",
- " - Romps (2017)\n",
- " - Murphy-Koop\n",
- " - Bolton\n",
- " - Wagner and Pruss (WP, 2002) is the default\n",
- "\t>>> eslf(273.16)\n",
- "\t611.657\n",
+ " \"\"\"Returns the saturation vapour pressure [Pa] over liquid given\n",
+ " the temperature. Temperatures can be in Celcius or Kelvin.\n",
+ " Formulas supported are\n",
+ " - Goff-Gratch (1994 Smithsonian Tables)\n",
+ " - Sonntag (1994)\n",
+ " - Flatau\n",
+ " - Magnus Tetens (MT)\n",
+ " - Romps (2017)\n",
+ " - Murphy-Koop\n",
+ " - Bolton\n",
+ " - Wagner and Pruss (WP, 2002) is the default\n",
+ " >>> eslf(273.16)\n",
+ " 611.657\n",
" \"\"\"\n",
" import numpy as np\n",
"\n",
- " x, scalar_input = thermo_input(T, 'Kelvin')\n",
+ " x, scalar_input = thermo_input(T, \"Kelvin\")\n",
"\n",
" if formula == \"flatau\":\n",
- " if (np.min(x) > 100): x = x-273.16\n",
- " np.maximum(x,-80.)\n",
- " c_es= np.asarray([0.6105851e+03, 0.4440316e+02, 0.1430341e+01, 0.2641412e-01,\n",
- " 0.2995057e-03,0.2031998e-05,0.6936113e-08,0.2564861e-11,-0.3704404e-13])\n",
- " es = np.polyval(c_es[::-1],x)\n",
+ " if np.min(x) > 100:\n",
+ " x = x - 273.16\n",
+ " np.maximum(x, -80.0)\n",
+ " c_es = np.asarray(\n",
+ " [\n",
+ " 0.6105851e03,\n",
+ " 0.4440316e02,\n",
+ " 0.1430341e01,\n",
+ " 0.2641412e-01,\n",
+ " 0.2995057e-03,\n",
+ " 0.2031998e-05,\n",
+ " 0.6936113e-08,\n",
+ " 0.2564861e-11,\n",
+ " -0.3704404e-13,\n",
+ " ]\n",
+ " )\n",
+ " es = np.polyval(c_es[::-1], x)\n",
" elif formula == \"bolton\":\n",
- " if (np.min(x) > 100): x = x-273.15\n",
- " es = 611.2*np.exp((17.67*x)/(243.5+x))\n",
+ " if np.min(x) > 100:\n",
+ " x = x - 273.15\n",
+ " es = 611.2 * np.exp((17.67 * x) / (243.5 + x))\n",
" elif formula == \"sonntag\":\n",
- " xx = -6096.9385/x + 16.635794 - 2.711193e-2*x + 1.673952e-5*x*x + 2.433502 * np.log(x)\n",
- " es = 100.*np.exp(xx)\n",
- " elif formula =='goff-gratch':\n",
- " x1 = 273.16/x\n",
- " x2 = 373.16/x\n",
- " xl = np.log10(1013.246 ) - 7.90298*(x2 - 1) + 5.02808*np.log10(x2) - 1.3816e-7*(10**(11.344*(1.-1./x2)) - 1.0) + 8.1328e-3 * (10**(-3.49149*(x2-1)) - 1.0)\n",
- " es =10**(xl+2) # plus 2 converts from hPa to Pa\n",
- " elif formula == 'wagner-pruss':\n",
- " vt = 1.-x/TvC\n",
- " es = PvC * np.exp(TvC/x * (-7.85951783*vt + 1.84408259*vt**1.5 - 11.7866497*vt**3 + 22.6807411*vt**3.5 - 15.9618719*vt**4 + 1.80122502*vt**7.5))\n",
- " elif formula == 'hardy98':\n",
- " y = -2.8365744e+3/(x*x) - 6.028076559e+3/x + 19.54263612 - 2.737830188e-2*x + 1.6261698e-5*x**2 + 7.0229056e-10*x**3 - 1.8680009e-13*x**4 + 2.7150305 * np.log(x)\n",
+ " xx = (\n",
+ " -6096.9385 / x\n",
+ " + 16.635794\n",
+ " - 2.711193e-2 * x\n",
+ " + 1.673952e-5 * x * x\n",
+ " + 2.433502 * np.log(x)\n",
+ " )\n",
+ " es = 100.0 * np.exp(xx)\n",
+ " elif formula == \"goff-gratch\":\n",
+ " x1 = 273.16 / x\n",
+ " x2 = 373.16 / x\n",
+ " xl = (\n",
+ " np.log10(1013.246)\n",
+ " - 7.90298 * (x2 - 1)\n",
+ " + 5.02808 * np.log10(x2)\n",
+ " - 1.3816e-7 * (10 ** (11.344 * (1.0 - 1.0 / x2)) - 1.0)\n",
+ " + 8.1328e-3 * (10 ** (-3.49149 * (x2 - 1)) - 1.0)\n",
+ " )\n",
+ " es = 10 ** (xl + 2) # plus 2 converts from hPa to Pa\n",
+ " elif formula == \"wagner-pruss\":\n",
+ " vt = 1.0 - x / TvC\n",
+ " es = PvC * np.exp(\n",
+ " TvC\n",
+ " / x\n",
+ " * (\n",
+ " -7.85951783 * vt\n",
+ " + 1.84408259 * vt**1.5\n",
+ " - 11.7866497 * vt**3\n",
+ " + 22.6807411 * vt**3.5\n",
+ " - 15.9618719 * vt**4\n",
+ " + 1.80122502 * vt**7.5\n",
+ " )\n",
+ " )\n",
+ " elif formula == \"hardy98\":\n",
+ " y = (\n",
+ " -2.8365744e3 / (x * x)\n",
+ " - 6.028076559e3 / x\n",
+ " + 19.54263612\n",
+ " - 2.737830188e-2 * x\n",
+ " + 1.6261698e-5 * x**2\n",
+ " + 7.0229056e-10 * x**3\n",
+ " - 1.8680009e-13 * x**4\n",
+ " + 2.7150305 * np.log(x)\n",
+ " )\n",
" es = np.exp(y)\n",
- " elif formula == 'romps':\n",
- " Rr = 461.\n",
+ " elif formula == \"romps\":\n",
+ " Rr = 461.0\n",
" cvl_r = 4119\n",
" cvv_r = 1418\n",
" cpv_r = cvv_r + Rr\n",
- " es = 611.65 * (x/TvT) **((cpv_r-cvl_r)/Rr) * np.exp((2.37403e6 - (cvv_r-cvl_r)*TvT)*(1/TvT - 1/x)/Rr)\n",
+ " es = (\n",
+ " 611.65\n",
+ " * (x / TvT) ** ((cpv_r - cvl_r) / Rr)\n",
+ " * np.exp((2.37403e6 - (cvv_r - cvl_r) * TvT) * (1 / TvT - 1 / x) / Rr)\n",
+ " )\n",
" elif formula == \"murphy-koop\":\n",
- " es = np.exp(54.842763 - 6763.22/x - 4.210*np.log(x) + 0.000367*x + np.tanh(0.0415*(x - 218.8)) * (53.878 - 1331.22/x - 9.44523 * np.log(x) + 0.014025*x))\n",
+ " es = np.exp(\n",
+ " 54.842763\n",
+ " - 6763.22 / x\n",
+ " - 4.210 * np.log(x)\n",
+ " + 0.000367 * x\n",
+ " + np.tanh(0.0415 * (x - 218.8))\n",
+ " * (53.878 - 1331.22 / x - 9.44523 * np.log(x) + 0.014025 * x)\n",
+ " )\n",
" elif formula == \"standard-analytic\":\n",
- " c1 = (cpv-cl)/Rv\n",
- " c2 = lvT/(Rv*TvT) - c1\n",
- " es = PvT * np.exp(c2*(1.-TvT/x)) * (x/TvT)**c1\n",
+ " c1 = (cpv - cl) / Rv\n",
+ " c2 = lvT / (Rv * TvT) - c1\n",
+ " es = PvT * np.exp(c2 * (1.0 - TvT / x)) * (x / TvT) ** c1\n",
" else:\n",
" exit(\"formula not supported\")\n",
"\n",
- " es = np.maximum(es,0)\n",
+ " es = np.maximum(es, 0)\n",
" if scalar_input:\n",
" return np.squeeze(es)\n",
" return es\n",
"\n",
+ "\n",
"def esif(T, formula=es_default):\n",
- " \"\"\" Returns the saturation vapour pressure [Pa] over ice given \n",
- "\tthe temperature. Temperatures can be in Celcius or Kelvin.\n",
- "\tuses the Goff-Gratch (1994 Smithsonian Tables) formula\n",
- "\t>>> esli(273.15)\n",
- "\t6.112\n",
- "m \"\"\"\n",
+ " \"\"\"Returns the saturation vapour pressure [Pa] over ice given\n",
+ " the temperature. Temperatures can be in Celcius or Kelvin.\n",
+ " uses the Goff-Gratch (1994 Smithsonian Tables) formula\n",
+ " >>> esli(273.15)\n",
+ " 6.112\n",
+ " m\"\"\"\n",
" import numpy as np\n",
"\n",
- " x, scalar_input = thermo_input(T, 'Kelvin')\n",
+ " x, scalar_input = thermo_input(T, \"Kelvin\")\n",
"\n",
" if formula == \"sonntag\":\n",
- " es = 100 * np.exp(24.7219 - 6024.5282/x + 0.010613868*x - 0.000013198825*x**2 - 0.49382577*np.log(x))\n",
+ " es = 100 * np.exp(\n",
+ " 24.7219\n",
+ " - 6024.5282 / x\n",
+ " + 0.010613868 * x\n",
+ " - 0.000013198825 * x**2\n",
+ " - 0.49382577 * np.log(x)\n",
+ " )\n",
" elif formula == \"goff-gratch\":\n",
- " x1 = 273.16/x\n",
- " xi = np.log10( 6.1071) - 9.09718*(x1 - 1) - 3.56654*np.log10(x1) + 0.876793*(1 - 1./x1)\n",
- " es = 10**(xi+2)\n",
- " elif formula == \"wagner-pruss\": #(actually wagner et al, 2011)\n",
- " a1 = -0.212144006e+2\n",
- " a2 = 0.273203819e+2\n",
- " a3 = -0.610598130e+1\n",
- " b1 = 0.333333333e-2\n",
- " b2 = 0.120666667e+1\n",
- " b3 = 0.170333333e+1\n",
- " theta = T/TvT\n",
- " es = PvT * np.exp((a1*theta**b1 + a2 * theta**b2 + a3 * theta**b3)/theta)\n",
+ " x1 = 273.16 / x\n",
+ " xi = (\n",
+ " np.log10(6.1071)\n",
+ " - 9.09718 * (x1 - 1)\n",
+ " - 3.56654 * np.log10(x1)\n",
+ " + 0.876793 * (1 - 1.0 / x1)\n",
+ " )\n",
+ " es = 10 ** (xi + 2)\n",
+ " elif formula == \"wagner-pruss\": # (actually wagner et al, 2011)\n",
+ " a1 = -0.212144006e2\n",
+ " a2 = 0.273203819e2\n",
+ " a3 = -0.610598130e1\n",
+ " b1 = 0.333333333e-2\n",
+ " b2 = 0.120666667e1\n",
+ " b3 = 0.170333333e1\n",
+ " theta = T / TvT\n",
+ " es = PvT * np.exp(\n",
+ " (a1 * theta**b1 + a2 * theta**b2 + a3 * theta**b3) / theta\n",
+ " )\n",
" elif formula == \"murphy-koop\":\n",
- " es = np.exp(9.550426 - 5723.265/x + 3.53068 * np.log(x) - 0.00728332*x)\n",
+ " es = np.exp(9.550426 - 5723.265 / x + 3.53068 * np.log(x) - 0.00728332 * x)\n",
" elif formula == \"romps\":\n",
- " Rr = 461.\n",
- " cvv_r = 1418.\n",
- " cvs_r = 1861.\n",
+ " Rr = 461.0\n",
+ " cvv_r = 1418.0\n",
+ " cvs_r = 1861.0\n",
" cpv_r = cvv_r + Rr\n",
- " es = 611.65 * (x/TvT) **((cpv_r-cvs_r)/Rr) * np.exp((2.37403e6 + 0.33373e6 - (cvv_r-cvs_r)*TvT)*(1/TvT - 1/x)/Rr)\n",
+ " es = (\n",
+ " 611.65\n",
+ " * (x / TvT) ** ((cpv_r - cvs_r) / Rr)\n",
+ " * np.exp(\n",
+ " (2.37403e6 + 0.33373e6 - (cvv_r - cvs_r) * TvT) * (1 / TvT - 1 / x) / Rr\n",
+ " )\n",
+ " )\n",
" elif formula == \"standard-analytic\":\n",
- " c1 = (cpv-ci)/Rv\n",
- " c2 = lsT/(Rv*TvT) - c1\n",
- " es = PvT * np.exp(c2*(1.-TvT/x)) * (x/TvT)**c1\n",
+ " c1 = (cpv - ci) / Rv\n",
+ " c2 = lsT / (Rv * TvT) - c1\n",
+ " es = PvT * np.exp(c2 * (1.0 - TvT / x)) * (x / TvT) ** c1\n",
" else:\n",
" exit(\"formula not supported\")\n",
"\n",
- " es = np.maximum(es,0)\n",
+ " es = np.maximum(es, 0)\n",
" if scalar_input:\n",
" return np.squeeze(es)\n",
" return es\n",
- " \n",
- "def esilf(T,formula=es_default):\n",
+ "\n",
+ "\n",
+ "def esilf(T, formula=es_default):\n",
" import numpy as np\n",
- " return np.minimum(esif(T,formula),eslf(T,formula))\n",
"\n",
- "def es(T,formula=es_default,state='liq'):\n",
+ " return np.minimum(esif(T, formula), eslf(T, formula))\n",
+ "\n",
+ "\n",
+ "def es(T, formula=es_default, state=\"liq\"):\n",
"\n",
" import numpy as np\n",
- " \n",
- " x, scalar_input = thermo_input(T, 'Kelvin')\n",
"\n",
- " if (state == 'liq'):\n",
- " return eslf(x,formula)\n",
- " if (state == 'ice'):\n",
- " return esif(x,formula)\n",
- " if (state == 'mxd'):\n",
- " return esilf(x,formula)\n",
+ " x, scalar_input = thermo_input(T, \"Kelvin\")\n",
"\n",
- "def des(T,formula=es_default,state='liq'):\n",
+ " if state == \"liq\":\n",
+ " return eslf(x, formula)\n",
+ " if state == \"ice\":\n",
+ " return esif(x, formula)\n",
+ " if state == \"mxd\":\n",
+ " return esilf(x, formula)\n",
+ "\n",
+ "\n",
+ "def des(T, formula=es_default, state=\"liq\"):\n",
"\n",
" import numpy as np\n",
- " \n",
- " x, scalar_input = thermo_input(T, 'Kelvin')\n",
- " dx = 0.01; xp = x+dx/2; xm = x-dx/2\n",
- " return (es(xp,formula,state)-es(xm,formula,state))/dx\n",
"\n",
- "def dlnesdlnT(T,formula=es_default,state='liq'):\n",
+ " x, scalar_input = thermo_input(T, \"Kelvin\")\n",
+ " dx = 0.01\n",
+ " xp = x + dx / 2\n",
+ " xm = x - dx / 2\n",
+ " return (es(xp, formula, state) - es(xm, formula, state)) / dx\n",
+ "\n",
+ "\n",
+ "def dlnesdlnT(T, formula=es_default, state=\"liq\"):\n",
"\n",
" import numpy as np\n",
- " \n",
- " x, scalar_input = thermo_input(T, 'Kelvin')\n",
- " dx = 0.01; xp = x+dx/2; xm = x-dx/2\n",
- " return ((es(xp,formula,state)-es(xm,formula,state))/es(x,formula,state) * (x/dx))\n",
- " \n",
- "def phase_change_enthalpy(Tx,fusion=False):\n",
- " \"\"\" Returns the enthlapy [J/g] of vaporization (default) of water vapor or \n",
+ "\n",
+ " x, scalar_input = thermo_input(T, \"Kelvin\")\n",
+ " dx = 0.01\n",
+ " xp = x + dx / 2\n",
+ " xm = x - dx / 2\n",
+ " return (\n",
+ " (es(xp, formula, state) - es(xm, formula, state))\n",
+ " / es(x, formula, state)\n",
+ " * (x / dx)\n",
+ " )\n",
+ "\n",
+ "\n",
+ "def phase_change_enthalpy(Tx, fusion=False):\n",
+ " \"\"\"Returns the enthlapy [J/g] of vaporization (default) of water vapor or\n",
" (if fusion=True) the fusion anthalpy. Input temperature can be in degC or Kelvin\n",
" >>> phase_change_enthalpy(273.15)\n",
" 2500.8e3\n",
" \"\"\"\n",
" import numpy as np\n",
"\n",
- " TC, scalar_input = thermo_input(Tx, 'Celcius')\n",
- " TK, scalar_input = thermo_input(Tx, 'Kelvin')\n",
+ " TC, scalar_input = thermo_input(Tx, \"Celcius\")\n",
+ " TK, scalar_input = thermo_input(Tx, \"Kelvin\")\n",
"\n",
- " if (fusion):\n",
- " el = lfT + (cl-ci)*(TK-TvT)\n",
+ " if fusion:\n",
+ " el = lfT + (cl - ci) * (TK - TvT)\n",
" else:\n",
- " el = lvT + (cpv-cl)*(TK-TvT)\n",
+ " el = lvT + (cpv - cl) * (TK - TvT)\n",
"\n",
" if scalar_input:\n",
" return np.squeeze(el)\n",
- " return el\n",
- " "
+ " return el"
]
},
{
@@ -312,35 +410,39 @@
"source": [
"import iapws\n",
"\n",
- "print ('Using IAPWS Version %s\\n'%(iapws.__version__,))\n",
- "T = np.arange(183.15,313.15)\n",
- "ci_iapws = np.full(len(T),np.nan)\n",
- "cl_iapws = np.full(len(T),np.nan)\n",
- "for i,Tx in enumerate(T):\n",
- " if (Tx < 283): ci_iapws[i] = iapws._iapws._Ice(Tx, 0.1)['cp']*1000 / ci\n",
- " if (Tx > 253.15): cl_iapws[i] = iapws._iapws._Liquid(Tx, 0.1)['cp']*1000 / cl\n",
- "\n",
- "fig = plt.figure(figsize=(4,3))\n",
- "\n",
- "ax1 = plt.subplot(1,1,1)\n",
- "ax1.set_xlabel('$T$ / K')\n",
- "ax1.set_ylabel('$c_\\mathrm{i}$ / %5.2f, $c_\\mathrm{l}$ / %5.2f'%(ci,cl))\n",
- "ax1.set_xticks([185,247.07,273.15,305.00])\n",
- "plt.scatter([247.065],[1.])\n",
- "plt.scatter([305.000],[1.])\n",
- "plt.plot(T,ci_iapws)\n",
- "plt.plot(T,cl_iapws)\n",
+ "print(\"Using IAPWS Version %s\\n\" % (iapws.__version__,))\n",
+ "T = np.arange(183.15, 313.15)\n",
+ "ci_iapws = np.full(len(T), np.nan)\n",
+ "cl_iapws = np.full(len(T), np.nan)\n",
+ "for i, Tx in enumerate(T):\n",
+ " if Tx < 283:\n",
+ " ci_iapws[i] = iapws._iapws._Ice(Tx, 0.1)[\"cp\"] * 1000 / ci\n",
+ " if Tx > 253.15:\n",
+ " cl_iapws[i] = iapws._iapws._Liquid(Tx, 0.1)[\"cp\"] * 1000 / cl\n",
+ "\n",
+ "fig = plt.figure(figsize=(4, 3))\n",
+ "\n",
+ "ax1 = plt.subplot(1, 1, 1)\n",
+ "ax1.set_xlabel(\"$T$ / K\")\n",
+ "ax1.set_ylabel(\"$c_\\mathrm{i}$ / %5.2f, $c_\\mathrm{l}$ / %5.2f\" % (ci, cl))\n",
+ "ax1.set_xticks([185, 247.07, 273.15, 305.00])\n",
+ "plt.scatter([247.065], [1.0])\n",
+ "plt.scatter([305.000], [1.0])\n",
+ "plt.plot(T, ci_iapws)\n",
+ "plt.plot(T, cl_iapws)\n",
"\n",
"sns.set_context(\"paper\", font_scale=1.2)\n",
"sns.despine(offset=10)\n",
"\n",
"plt.tight_layout()\n",
- "fig.savefig(plot_dir+'cp-Tdependance.pdf')\n",
+ "fig.savefig(plot_dir + \"cp-Tdependance.pdf\")\n",
"\n",
- "TK = np.arange(273.15,315.15,0.01)\n",
+ "TK = np.arange(273.15, 315.15, 0.01)\n",
"es_iapws = np.zeros(len(TK))\n",
"for i, x in enumerate(TK):\n",
- " es_iapws[i] = iapws.iapws97._PSat_T(x) *1.e6 #Temperature, [K]; Returns:Pressure, [MPa]"
+ " es_iapws[i] = (\n",
+ " iapws.iapws97._PSat_T(x) * 1.0e6\n",
+ " ) # Temperature, [K]; Returns:Pressure, [MPa]"
]
},
{
@@ -372,67 +474,102 @@
],
"source": [
"import pandas as pd\n",
- "sia_dir = './data/'\n",
- "d0 = pd.read_csv(sia_dir + 'psat.dat',sep=' ',names=['T','Psat_liq','Psat_ice'])\n",
- "x0 = d0.to_xarray()\n",
- "d1 = pd.read_csv(sia_dir + 'cp-liq-vap.dat',sep=' ',names=['T','liq_density','vap_density','cp_liq','cp_vap','lv'])\n",
- "x1 = d1.to_xarray()\n",
- "d2 = pd.read_csv(sia_dir + 'cp-ice-vap.dat',sep=' ',names=['T','liq_density','vap_density','cp_ice','cp_vap','ls'])\n",
- "x2 = d2.to_xarray()\n",
- "\n",
- "fig = plt.figure(figsize=(7,14/1.610834))\n",
- "\n",
- "ax1 = plt.subplot(2,1,2)\n",
- "ax1.set_ylabel('difference / %')\n",
- "ax1.set_xlabel('T / K')\n",
- "\n",
- "formula = 'wagner-pruss'\n",
- "es_r = es(x0.T,formula=formula,state='ice')\n",
- "diff = es_r/x0.Psat_ice\n",
- "plt.plot(x0.T,100*(diff.where(diff>1.e-4)-1),c='dodgerblue',label=formula)\n",
- "es_r = es(x0.T,formula=formula,state='liq')\n",
- "diff = es_r/x0.Psat_liq\n",
- "plt.plot(x0.T,100*(diff.where(diff>1.e-4)-1),c='orange',label=formula)\n",
- "\n",
- "formula = 'romps'\n",
- "es_r = es(x0.T,formula=formula,state='ice')\n",
- "diff = es_r/x0.Psat_ice\n",
- "plt.plot(x0.T,100*(diff.where(diff>1.e-4)-1),c='dodgerblue',ls='dashed',label=formula)\n",
- "es_r = es(x0.T,formula=formula,state='liq')\n",
- "diff = es_r/x0.Psat_liq\n",
- "plt.plot(x0.T,100*(diff.where(diff>1.e-4)-1),c='orange',ls='dashed',label=formula)\n",
- "\n",
- "formula = 'murphy-koop'\n",
- "es_r = es(x0.T,formula=formula,state='ice')\n",
- "diff = es_r/x0.Psat_ice\n",
- "plt.plot(x0.T,100*(diff.where(diff>1.e-4)-1),c='dodgerblue',ls='dotted',label=formula)\n",
- "es_r = es(x0.T,formula=formula,state='liq')\n",
- "diff = es_r/x0.Psat_liq\n",
- "plt.plot(x0.T,100*(diff.where(diff>1.e-4)-1),c='orange',ls='dotted',label=formula)\n",
- "plt.legend(loc=\"best\",ncol=3)\n",
- "\n",
- "###\n",
- "ax2 = plt.subplot(2,1,1)\n",
- "ax2.set_ylabel('difference / %')\n",
- "ax2.set_xlabel('T / K')\n",
- "ax2.set_ylim(0.8,1.2)\n",
"\n",
- "plt.plot(x1.T,x1.cp_vap/cpv,c='green',ls='solid',label='$c_{p,\\mathrm{vap}}$ (vap-liq)')\n",
- "plt.plot(x2.T,x2.cp_vap/cpv,c='green',ls='dashed',label='$c_{p,\\mathrm{vap}}$ (vap-ice)')\n",
+ "sia_dir = \"./data/\"\n",
+ "d0 = pd.read_csv(sia_dir + \"psat.dat\", sep=\" \", names=[\"T\", \"Psat_liq\", \"Psat_ice\"])\n",
+ "x0 = d0.to_xarray()\n",
+ "d1 = pd.read_csv(\n",
+ " sia_dir + \"cp-liq-vap.dat\",\n",
+ " sep=\" \",\n",
+ " names=[\"T\", \"liq_density\", \"vap_density\", \"cp_liq\", \"cp_vap\", \"lv\"],\n",
+ ")\n",
+ "x1 = d1.to_xarray()\n",
+ "d2 = pd.read_csv(\n",
+ " sia_dir + \"cp-ice-vap.dat\",\n",
+ " sep=\" \",\n",
+ " names=[\"T\", \"liq_density\", \"vap_density\", \"cp_ice\", \"cp_vap\", \"ls\"],\n",
+ ")\n",
+ "x2 = d2.to_xarray()\n",
+ "\n",
+ "fig = plt.figure(figsize=(7, 14 / 1.610834))\n",
+ "\n",
+ "ax1 = plt.subplot(2, 1, 2)\n",
+ "ax1.set_ylabel(\"difference / %\")\n",
+ "ax1.set_xlabel(\"T / K\")\n",
+ "\n",
+ "formula = \"wagner-pruss\"\n",
+ "es_r = es(x0.T, formula=formula, state=\"ice\")\n",
+ "diff = es_r / x0.Psat_ice\n",
+ "plt.plot(x0.T, 100 * (diff.where(diff > 1.0e-4) - 1), c=\"dodgerblue\", label=formula)\n",
+ "es_r = es(x0.T, formula=formula, state=\"liq\")\n",
+ "diff = es_r / x0.Psat_liq\n",
+ "plt.plot(x0.T, 100 * (diff.where(diff > 1.0e-4) - 1), c=\"orange\", label=formula)\n",
+ "\n",
+ "formula = \"romps\"\n",
+ "es_r = es(x0.T, formula=formula, state=\"ice\")\n",
+ "diff = es_r / x0.Psat_ice\n",
+ "plt.plot(\n",
+ " x0.T,\n",
+ " 100 * (diff.where(diff > 1.0e-4) - 1),\n",
+ " c=\"dodgerblue\",\n",
+ " ls=\"dashed\",\n",
+ " label=formula,\n",
+ ")\n",
+ "es_r = es(x0.T, formula=formula, state=\"liq\")\n",
+ "diff = es_r / x0.Psat_liq\n",
+ "plt.plot(\n",
+ " x0.T, 100 * (diff.where(diff > 1.0e-4) - 1), c=\"orange\", ls=\"dashed\", label=formula\n",
+ ")\n",
+ "\n",
+ "formula = \"murphy-koop\"\n",
+ "es_r = es(x0.T, formula=formula, state=\"ice\")\n",
+ "diff = es_r / x0.Psat_ice\n",
+ "plt.plot(\n",
+ " x0.T,\n",
+ " 100 * (diff.where(diff > 1.0e-4) - 1),\n",
+ " c=\"dodgerblue\",\n",
+ " ls=\"dotted\",\n",
+ " label=formula,\n",
+ ")\n",
+ "es_r = es(x0.T, formula=formula, state=\"liq\")\n",
+ "diff = es_r / x0.Psat_liq\n",
+ "plt.plot(\n",
+ " x0.T, 100 * (diff.where(diff > 1.0e-4) - 1), c=\"orange\", ls=\"dotted\", label=formula\n",
+ ")\n",
+ "plt.legend(loc=\"best\", ncol=3)\n",
"\n",
- "plt.plot(x1.T,x1.cp_liq/cl,c='orange',ls='solid',label='$c_{p,\\mathrm{liq}}$')\n",
- "plt.plot(x2.T,x2.cp_ice/ci,c='dodgerblue',ls='solid',label='$c_{p,\\mathrm{ice}}$')\n",
- "\n",
- "lvx = phase_change_enthalpy(x1.T,fusion=False)\n",
- "lsx = phase_change_enthalpy(x2.T,fusion=True) + phase_change_enthalpy(x2.T,fusion=False)\n",
- "\n",
- "plt.plot(x1.T,x1.lv/lvx,c='gray',ls='solid',label='$\\\\ell_v$')\n",
- "plt.plot(x2.T,x2.ls/lsx,c='gray',ls='dashed',label='$\\\\ell_s$')\n",
- "\n",
- "plt.legend(loc=\"lower right\",ncol=3)\n",
+ "###\n",
+ "ax2 = plt.subplot(2, 1, 1)\n",
+ "ax2.set_ylabel(\"difference / %\")\n",
+ "ax2.set_xlabel(\"T / K\")\n",
+ "ax2.set_ylim(0.8, 1.2)\n",
+ "\n",
+ "plt.plot(\n",
+ " x1.T, x1.cp_vap / cpv, c=\"green\", ls=\"solid\", label=\"$c_{p,\\mathrm{vap}}$ (vap-liq)\"\n",
+ ")\n",
+ "plt.plot(\n",
+ " x2.T,\n",
+ " x2.cp_vap / cpv,\n",
+ " c=\"green\",\n",
+ " ls=\"dashed\",\n",
+ " label=\"$c_{p,\\mathrm{vap}}$ (vap-ice)\",\n",
+ ")\n",
+ "\n",
+ "plt.plot(x1.T, x1.cp_liq / cl, c=\"orange\", ls=\"solid\", label=\"$c_{p,\\mathrm{liq}}$\")\n",
+ "plt.plot(x2.T, x2.cp_ice / ci, c=\"dodgerblue\", ls=\"solid\", label=\"$c_{p,\\mathrm{ice}}$\")\n",
+ "\n",
+ "lvx = phase_change_enthalpy(x1.T, fusion=False)\n",
+ "lsx = phase_change_enthalpy(x2.T, fusion=True) + phase_change_enthalpy(\n",
+ " x2.T, fusion=False\n",
+ ")\n",
+ "\n",
+ "plt.plot(x1.T, x1.lv / lvx, c=\"gray\", ls=\"solid\", label=\"$\\\\ell_v$\")\n",
+ "plt.plot(x2.T, x2.ls / lsx, c=\"gray\", ls=\"dashed\", label=\"$\\\\ell_s$\")\n",
+ "\n",
+ "plt.legend(loc=\"lower right\", ncol=3)\n",
"sns.set_context(\"paper\")\n",
"sns.despine(offset=10)\n",
- "plt.tight_layout()\n"
+ "plt.tight_layout()"
]
},
{
@@ -481,41 +618,41 @@
}
],
"source": [
- "state = 'liq'\n",
- "fig = plt.figure(figsize=(10,5))\n",
- "ax1 = plt.subplot(1,1,1)\n",
- "ax1.set_xlabel('$T$ / K')\n",
- "ax1.set_ylabel('$e_{\\mathrm{s,x}}/e_{\\mathrm{s,ref}} - 1$')\n",
- "ax1.set_yscale('log')\n",
+ "state = \"liq\"\n",
+ "fig = plt.figure(figsize=(10, 5))\n",
+ "ax1 = plt.subplot(1, 1, 1)\n",
+ "ax1.set_xlabel(\"$T$ / K\")\n",
+ "ax1.set_ylabel(\"$e_{\\mathrm{s,x}}/e_{\\mathrm{s,ref}} - 1$\")\n",
+ "ax1.set_yscale(\"log\")\n",
"\n",
"es_ref = es_iapws\n",
- "es_w = es(TK,formula=\"wagner-pruss\",state=state)\n",
- "es_r = es(TK,formula='romps',state=state)\n",
- "es_g = es(TK,formula='goff-gratch',state=state)\n",
- "es_m = es(TK,formula='murphy-koop',state=state)\n",
- "es_s = es(TK,formula='sonntag',state=state)\n",
- "es_b = es(TK,formula='bolton',state=state)\n",
- "es_f = es(TK,formula='flatau',state=state)\n",
- "es_h = es(TK,formula='hardy98',state=state)\n",
- "es_a = es(TK,formula='standard-analytic',state=state)\n",
- "\n",
- "plt.plot(TK,np.abs(es_h/es_ref-1),c='tab:blue',ls='solid',label='Hardy (1998)')\n",
- "plt.plot(TK,np.abs(es_f/es_ref-1),c='tab:orange',label='Flatau (1992)')\n",
- "plt.plot(TK,np.abs(es_g/es_ref-1),c='tab:green',label='Goff-Gratch (1957)')\n",
- "plt.plot(TK,np.abs(es_b/es_ref-1),c='tab:red',ls='dotted',label='Bolton (1980)')\n",
- "\n",
- "plt.plot(TK,np.abs(es_r/es_ref-1),c='tab:purple',label='Romps (2017)')\n",
- "plt.plot(TK,np.abs(es_s/es_ref-1),c='tab:grey',label='Sonntag (1990)')\n",
- "plt.plot(TK,np.abs(es_m/es_ref-1),c='tab:pink',label='Murphy-Koop (2005)')\n",
- "plt.plot(TK,np.abs(es_w/es_ref-1),c='tab:brown',label='Wagner-Pruss (2002)')\n",
- "plt.plot(TK,np.abs(es_a/es_ref-1),c='tab:purple',ls='dotted',label='Analytic')\n",
- "\n",
- "plt.legend(loc=\"lower right\",ncol=3)\n",
+ "es_w = es(TK, formula=\"wagner-pruss\", state=state)\n",
+ "es_r = es(TK, formula=\"romps\", state=state)\n",
+ "es_g = es(TK, formula=\"goff-gratch\", state=state)\n",
+ "es_m = es(TK, formula=\"murphy-koop\", state=state)\n",
+ "es_s = es(TK, formula=\"sonntag\", state=state)\n",
+ "es_b = es(TK, formula=\"bolton\", state=state)\n",
+ "es_f = es(TK, formula=\"flatau\", state=state)\n",
+ "es_h = es(TK, formula=\"hardy98\", state=state)\n",
+ "es_a = es(TK, formula=\"standard-analytic\", state=state)\n",
+ "\n",
+ "plt.plot(TK, np.abs(es_h / es_ref - 1), c=\"tab:blue\", ls=\"solid\", label=\"Hardy (1998)\")\n",
+ "plt.plot(TK, np.abs(es_f / es_ref - 1), c=\"tab:orange\", label=\"Flatau (1992)\")\n",
+ "plt.plot(TK, np.abs(es_g / es_ref - 1), c=\"tab:green\", label=\"Goff-Gratch (1957)\")\n",
+ "plt.plot(TK, np.abs(es_b / es_ref - 1), c=\"tab:red\", ls=\"dotted\", label=\"Bolton (1980)\")\n",
+ "\n",
+ "plt.plot(TK, np.abs(es_r / es_ref - 1), c=\"tab:purple\", label=\"Romps (2017)\")\n",
+ "plt.plot(TK, np.abs(es_s / es_ref - 1), c=\"tab:grey\", label=\"Sonntag (1990)\")\n",
+ "plt.plot(TK, np.abs(es_m / es_ref - 1), c=\"tab:pink\", label=\"Murphy-Koop (2005)\")\n",
+ "plt.plot(TK, np.abs(es_w / es_ref - 1), c=\"tab:brown\", label=\"Wagner-Pruss (2002)\")\n",
+ "plt.plot(TK, np.abs(es_a / es_ref - 1), c=\"tab:purple\", ls=\"dotted\", label=\"Analytic\")\n",
+ "\n",
+ "plt.legend(loc=\"lower right\", ncol=3)\n",
"\n",
"sns.set_context(\"paper\", font_scale=1.2)\n",
"sns.despine(offset=10)\n",
"\n",
- "fig.savefig(plot_dir+'es_l-error.pdf')"
+ "fig.savefig(plot_dir + \"es_l-error.pdf\")"
]
},
{
@@ -535,45 +672,45 @@
"metadata": {},
"outputs": [],
"source": [
- "state = 'liq'\n",
- "fig = plt.figure(figsize=(10,5))\n",
- "ax1 = plt.subplot(1,1,1)\n",
- "ax1.set_xlabel('$T$ / K')\n",
- "ax1.set_ylabel('$e_{\\mathrm{s,x}}/e_{\\mathrm{s,ref}} - 1$')\n",
- "ax1.set_yscale('log')\n",
- "\n",
- "TK = np.arange(180,320,0.5)\n",
- "\n",
- "es_w = es(TK,formula=\"wagner-pruss\",state=state)\n",
- "es_r = es(TK,formula='romps',state=state)\n",
- "es_g = es(TK,formula='goff-gratch',state=state)\n",
- "es_m = es(TK,formula='murphy-koop',state=state)\n",
- "es_s = es(TK,formula='sonntag',state=state)\n",
- "es_b = es(TK,formula='bolton',state=state)\n",
- "es_f = es(TK,formula='flatau',state=state)\n",
- "es_h = es(TK,formula='hardy98',state=state)\n",
- "es_a = es(TK,formula='standard-analytic',state=state)\n",
+ "state = \"liq\"\n",
+ "fig = plt.figure(figsize=(10, 5))\n",
+ "ax1 = plt.subplot(1, 1, 1)\n",
+ "ax1.set_xlabel(\"$T$ / K\")\n",
+ "ax1.set_ylabel(\"$e_{\\mathrm{s,x}}/e_{\\mathrm{s,ref}} - 1$\")\n",
+ "ax1.set_yscale(\"log\")\n",
+ "\n",
+ "TK = np.arange(180, 320, 0.5)\n",
+ "\n",
+ "es_w = es(TK, formula=\"wagner-pruss\", state=state)\n",
+ "es_r = es(TK, formula=\"romps\", state=state)\n",
+ "es_g = es(TK, formula=\"goff-gratch\", state=state)\n",
+ "es_m = es(TK, formula=\"murphy-koop\", state=state)\n",
+ "es_s = es(TK, formula=\"sonntag\", state=state)\n",
+ "es_b = es(TK, formula=\"bolton\", state=state)\n",
+ "es_f = es(TK, formula=\"flatau\", state=state)\n",
+ "es_h = es(TK, formula=\"hardy98\", state=state)\n",
+ "es_a = es(TK, formula=\"standard-analytic\", state=state)\n",
"\n",
"es_ref = es_w\n",
"\n",
- "plt.plot(TK,np.abs(es_h/es_ref-1),c='tab:blue',ls='solid',label='Hardy (1998)')\n",
- "plt.plot(TK,np.abs(es_f/es_ref-1),c='tab:orange',label='Flatau (1992)')\n",
- "plt.plot(TK,np.abs(es_g/es_ref-1),c='tab:green',label='Goff-Gratch (1957)')\n",
- "plt.plot(TK,np.abs(es_b/es_ref-1),c='tab:red',ls='dotted',label='Bolton (1980)')\n",
+ "plt.plot(TK, np.abs(es_h / es_ref - 1), c=\"tab:blue\", ls=\"solid\", label=\"Hardy (1998)\")\n",
+ "plt.plot(TK, np.abs(es_f / es_ref - 1), c=\"tab:orange\", label=\"Flatau (1992)\")\n",
+ "plt.plot(TK, np.abs(es_g / es_ref - 1), c=\"tab:green\", label=\"Goff-Gratch (1957)\")\n",
+ "plt.plot(TK, np.abs(es_b / es_ref - 1), c=\"tab:red\", ls=\"dotted\", label=\"Bolton (1980)\")\n",
"\n",
- "plt.plot(TK,np.abs(es_r/es_ref-1),c='tab:purple',label='Romps (2017)')\n",
- "plt.plot(TK,np.abs(es_s/es_ref-1),c='tab:grey',label='Sonntag (1990)')\n",
- "plt.plot(TK,np.abs(es_m/es_ref-1),c='tab:pink',label='Murphy-Koop (2005)')\n",
- "plt.plot(TK,np.abs(es_a/es_ref-1),c='tab:purple',ls='dotted',label='Analytic')\n",
+ "plt.plot(TK, np.abs(es_r / es_ref - 1), c=\"tab:purple\", label=\"Romps (2017)\")\n",
+ "plt.plot(TK, np.abs(es_s / es_ref - 1), c=\"tab:grey\", label=\"Sonntag (1990)\")\n",
+ "plt.plot(TK, np.abs(es_m / es_ref - 1), c=\"tab:pink\", label=\"Murphy-Koop (2005)\")\n",
+ "plt.plot(TK, np.abs(es_a / es_ref - 1), c=\"tab:purple\", ls=\"dotted\", label=\"Analytic\")\n",
"\n",
- "#plt.plot(TK,np.abs(es_w/es_ref-1),c='tab:olive',label='Wagner-Pruss (2002)')\n",
+ "# plt.plot(TK,np.abs(es_w/es_ref-1),c='tab:olive',label='Wagner-Pruss (2002)')\n",
"\n",
- "plt.legend(loc=\"lower left\",ncol=2)\n",
+ "plt.legend(loc=\"lower left\", ncol=2)\n",
"\n",
"sns.set_context(\"paper\", font_scale=1.2)\n",
"sns.despine(offset=10)\n",
"\n",
- "fig.savefig(plot_dir+'es_lsc-error.pdf')"
+ "fig.savefig(plot_dir + \"es_lsc-error.pdf\")"
]
},
{
@@ -591,37 +728,37 @@
"metadata": {},
"outputs": [],
"source": [
- "state = 'ice'\n",
- "fig = plt.figure(figsize=(10,5))\n",
- "ax1 = plt.subplot(1,1,1)\n",
- "ax1.set_xlabel('$T$ / K')\n",
- "ax1.set_ylabel('$e_{\\mathrm{s,x}}/e_{\\mathrm{s,ref}} - 1$')\n",
- "ax1.set_yscale('log')\n",
- "\n",
- "TK = np.arange(180,320,0.5)\n",
- "\n",
- "es_w = es(TK,formula=\"wagner-pruss\",state=state)\n",
- "es_r = es(TK,formula='romps',state=state)\n",
- "es_g = es(TK,formula='goff-gratch',state=state)\n",
- "es_m = es(TK,formula='murphy-koop',state=state)\n",
- "es_s = es(TK,formula='sonntag',state=state)\n",
- "es_a = es(TK,formula='standard-analytic',state=state)\n",
+ "state = \"ice\"\n",
+ "fig = plt.figure(figsize=(10, 5))\n",
+ "ax1 = plt.subplot(1, 1, 1)\n",
+ "ax1.set_xlabel(\"$T$ / K\")\n",
+ "ax1.set_ylabel(\"$e_{\\mathrm{s,x}}/e_{\\mathrm{s,ref}} - 1$\")\n",
+ "ax1.set_yscale(\"log\")\n",
+ "\n",
+ "TK = np.arange(180, 320, 0.5)\n",
+ "\n",
+ "es_w = es(TK, formula=\"wagner-pruss\", state=state)\n",
+ "es_r = es(TK, formula=\"romps\", state=state)\n",
+ "es_g = es(TK, formula=\"goff-gratch\", state=state)\n",
+ "es_m = es(TK, formula=\"murphy-koop\", state=state)\n",
+ "es_s = es(TK, formula=\"sonntag\", state=state)\n",
+ "es_a = es(TK, formula=\"standard-analytic\", state=state)\n",
"es_ref = es_w\n",
"\n",
- "plt.plot(TK,np.abs(es_g/es_ref-1),c='tab:green',label='Goff-Gratch (1957)')\n",
- "plt.plot(TK,np.abs(es_r/es_ref-1),c='tab:purple',label='Romps (2017)')\n",
- "plt.plot(TK,np.abs(es_s/es_ref-1),c='tab:grey',label='Sonntag (1990)')\n",
- "plt.plot(TK,np.abs(es_m/es_ref-1),c='tab:pink',label='Murphy-Koop (2005)')\n",
- "plt.plot(TK,np.abs(es_a/es_ref-1),c='tab:purple',ls='dotted',label='Analytic')\n",
+ "plt.plot(TK, np.abs(es_g / es_ref - 1), c=\"tab:green\", label=\"Goff-Gratch (1957)\")\n",
+ "plt.plot(TK, np.abs(es_r / es_ref - 1), c=\"tab:purple\", label=\"Romps (2017)\")\n",
+ "plt.plot(TK, np.abs(es_s / es_ref - 1), c=\"tab:grey\", label=\"Sonntag (1990)\")\n",
+ "plt.plot(TK, np.abs(es_m / es_ref - 1), c=\"tab:pink\", label=\"Murphy-Koop (2005)\")\n",
+ "plt.plot(TK, np.abs(es_a / es_ref - 1), c=\"tab:purple\", ls=\"dotted\", label=\"Analytic\")\n",
"\n",
- "#plt.plot(TK,np.abs(es_w/es_ref-1),c='tab:olive',label='Wagner-Pruss (2002)')\n",
+ "# plt.plot(TK,np.abs(es_w/es_ref-1),c='tab:olive',label='Wagner-Pruss (2002)')\n",
"\n",
- "plt.legend(loc=\"lower left\",ncol=2)\n",
+ "plt.legend(loc=\"lower left\", ncol=2)\n",
"\n",
"sns.set_context(\"paper\", font_scale=1.2)\n",
"sns.despine(offset=10)\n",
"\n",
- "fig.savefig(plot_dir+'es_i-error.pdf')"
+ "fig.savefig(plot_dir + \"es_i-error.pdf\")"
]
},
{
@@ -651,70 +788,72 @@
"metadata": {},
"outputs": [],
"source": [
- "state = 'liq'\n",
+ "state = \"liq\"\n",
"\n",
- "fig = plt.figure(figsize=(10,10))\n",
+ "fig = plt.figure(figsize=(10, 10))\n",
"\n",
- "ax1 = plt.subplot(2,1,1)\n",
+ "ax1 = plt.subplot(2, 1, 1)\n",
"\n",
- "ax1.set_ylabel('$|\\mathrm{CC}_\\mathrm{liq} - 1|$')\n",
- "ax1.set_yscale('log')\n",
+ "ax1.set_ylabel(\"$|\\mathrm{CC}_\\mathrm{liq} - 1|$\")\n",
+ "ax1.set_yscale(\"log\")\n",
"ax1.set_xticklabels([])\n",
"\n",
- "TK = np.arange(180,320,0.5)\n",
- "\n",
- "lv = phase_change_enthalpy(TK)\n",
- "if (state == 'ice'): lv += phase_change_enthalpy(TK,fusion=True)\n",
- "\n",
- "y = lv/(Rv * TK)\n",
- "cc_w = dlnesdlnT(TK,formula=\"wagner-pruss\",state=state) / y\n",
- "cc_r = dlnesdlnT(TK,formula='romps',state=state) /y\n",
- "cc_g = dlnesdlnT(TK,formula='goff-gratch',state=state) /y\n",
- "cc_m = dlnesdlnT(TK,formula='murphy-koop',state=state) /y\n",
- "cc_s = dlnesdlnT(TK,formula='sonntag',state=state) /y\n",
- "cc_h = dlnesdlnT(TK,formula='hardy98',state=state) /y\n",
- "cc_a = dlnesdlnT(TK,formula='standard-analytic',state=state) /y\n",
- "\n",
- "plt.plot(TK,np.abs(cc_h/1 -1.),c='tab:blue',label='Hardy (1998)')\n",
- "plt.plot(TK,np.abs(cc_g/1 -1.),c='tab:green',label='Goff-Gratch (1957)')\n",
- "plt.plot(TK,np.abs(cc_r/1 -1.),c='tab:purple',label='Romps (2017)')\n",
- "plt.plot(TK,np.abs(cc_s/1 -1.),c='tab:grey',label='Sonntag (1990)')\n",
- "plt.plot(TK,np.abs(cc_m/1 -1.),c='tab:pink',label='Murphy-Koop (2005)')\n",
- "plt.plot(TK,np.abs(cc_w/1 -1.),c='tab:olive',label='Wagner-Pruss (2002)')\n",
- "plt.plot(TK,np.abs(cc_a/1 -1.),c='tab:purple',ls='dotted',label='Analytic')\n",
- "\n",
- "plt.legend(loc=\"lower left\",ncol=1)\n",
- "\n",
- "state = 'ice'\n",
- "TK = np.arange(180,320,0.5)\n",
- "\n",
- "lv = phase_change_enthalpy(TK)\n",
- "if (state == 'ice'): lv = phase_change_enthalpy(TK,fusion=True) + phase_change_enthalpy(TK)\n",
- "\n",
- "y = lv/(Rv * TK)\n",
- "cc_w = dlnesdlnT(TK,formula=\"wagner-pruss\",state=state) / y\n",
- "cc_r = dlnesdlnT(TK,formula='romps',state=state) /y\n",
- "cc_g = dlnesdlnT(TK,formula='goff-gratch',state=state) /y\n",
- "cc_m = dlnesdlnT(TK,formula='murphy-koop',state=state) /y\n",
- "cc_s = dlnesdlnT(TK,formula='sonntag',state=state) /y\n",
- "cc_a = dlnesdlnT(TK,formula='standard-analytic',state=state) /y\n",
- "\n",
- "ax2 = plt.subplot(2,1,2)\n",
- "ax2.set_xlabel('$T$ / K')\n",
- "ax2.set_ylabel('$|\\mathrm{CC}_\\mathrm{ice} - 1|$')\n",
- "ax2.set_yscale('log')\n",
- "\n",
- "plt.plot(TK,np.abs(cc_g/1 -1.),c='tab:green',label='Goff-Gratch (1957)')\n",
- "plt.plot(TK,np.abs(cc_r/1 -1.),c='tab:purple',label='Romps (2017)')\n",
- "plt.plot(TK,np.abs(cc_s/1 -1.),c='tab:grey',label='Sonntag (1990)')\n",
- "plt.plot(TK,np.abs(cc_m/1 -1.),c='tab:pink',label='Murphy-Koop (2005)')\n",
- "plt.plot(TK,np.abs(cc_w/1 -1.),c='tab:olive',label='Wagner-Pruss (2002)')\n",
- "plt.plot(TK,np.abs(cc_a/1. -1.),c='tab:purple',ls='dotted',label='Analytic')\n",
+ "TK = np.arange(180, 320, 0.5)\n",
+ "\n",
+ "lv = phase_change_enthalpy(TK)\n",
+ "if state == \"ice\":\n",
+ " lv += phase_change_enthalpy(TK, fusion=True)\n",
+ "\n",
+ "y = lv / (Rv * TK)\n",
+ "cc_w = dlnesdlnT(TK, formula=\"wagner-pruss\", state=state) / y\n",
+ "cc_r = dlnesdlnT(TK, formula=\"romps\", state=state) / y\n",
+ "cc_g = dlnesdlnT(TK, formula=\"goff-gratch\", state=state) / y\n",
+ "cc_m = dlnesdlnT(TK, formula=\"murphy-koop\", state=state) / y\n",
+ "cc_s = dlnesdlnT(TK, formula=\"sonntag\", state=state) / y\n",
+ "cc_h = dlnesdlnT(TK, formula=\"hardy98\", state=state) / y\n",
+ "cc_a = dlnesdlnT(TK, formula=\"standard-analytic\", state=state) / y\n",
+ "\n",
+ "plt.plot(TK, np.abs(cc_h / 1 - 1.0), c=\"tab:blue\", label=\"Hardy (1998)\")\n",
+ "plt.plot(TK, np.abs(cc_g / 1 - 1.0), c=\"tab:green\", label=\"Goff-Gratch (1957)\")\n",
+ "plt.plot(TK, np.abs(cc_r / 1 - 1.0), c=\"tab:purple\", label=\"Romps (2017)\")\n",
+ "plt.plot(TK, np.abs(cc_s / 1 - 1.0), c=\"tab:grey\", label=\"Sonntag (1990)\")\n",
+ "plt.plot(TK, np.abs(cc_m / 1 - 1.0), c=\"tab:pink\", label=\"Murphy-Koop (2005)\")\n",
+ "plt.plot(TK, np.abs(cc_w / 1 - 1.0), c=\"tab:olive\", label=\"Wagner-Pruss (2002)\")\n",
+ "plt.plot(TK, np.abs(cc_a / 1 - 1.0), c=\"tab:purple\", ls=\"dotted\", label=\"Analytic\")\n",
+ "\n",
+ "plt.legend(loc=\"lower left\", ncol=1)\n",
+ "\n",
+ "state = \"ice\"\n",
+ "TK = np.arange(180, 320, 0.5)\n",
+ "\n",
+ "lv = phase_change_enthalpy(TK)\n",
+ "if state == \"ice\":\n",
+ " lv = phase_change_enthalpy(TK, fusion=True) + phase_change_enthalpy(TK)\n",
+ "\n",
+ "y = lv / (Rv * TK)\n",
+ "cc_w = dlnesdlnT(TK, formula=\"wagner-pruss\", state=state) / y\n",
+ "cc_r = dlnesdlnT(TK, formula=\"romps\", state=state) / y\n",
+ "cc_g = dlnesdlnT(TK, formula=\"goff-gratch\", state=state) / y\n",
+ "cc_m = dlnesdlnT(TK, formula=\"murphy-koop\", state=state) / y\n",
+ "cc_s = dlnesdlnT(TK, formula=\"sonntag\", state=state) / y\n",
+ "cc_a = dlnesdlnT(TK, formula=\"standard-analytic\", state=state) / y\n",
+ "\n",
+ "ax2 = plt.subplot(2, 1, 2)\n",
+ "ax2.set_xlabel(\"$T$ / K\")\n",
+ "ax2.set_ylabel(\"$|\\mathrm{CC}_\\mathrm{ice} - 1|$\")\n",
+ "ax2.set_yscale(\"log\")\n",
+ "\n",
+ "plt.plot(TK, np.abs(cc_g / 1 - 1.0), c=\"tab:green\", label=\"Goff-Gratch (1957)\")\n",
+ "plt.plot(TK, np.abs(cc_r / 1 - 1.0), c=\"tab:purple\", label=\"Romps (2017)\")\n",
+ "plt.plot(TK, np.abs(cc_s / 1 - 1.0), c=\"tab:grey\", label=\"Sonntag (1990)\")\n",
+ "plt.plot(TK, np.abs(cc_m / 1 - 1.0), c=\"tab:pink\", label=\"Murphy-Koop (2005)\")\n",
+ "plt.plot(TK, np.abs(cc_w / 1 - 1.0), c=\"tab:olive\", label=\"Wagner-Pruss (2002)\")\n",
+ "plt.plot(TK, np.abs(cc_a / 1.0 - 1.0), c=\"tab:purple\", ls=\"dotted\", label=\"Analytic\")\n",
"\n",
"sns.set_context(\"paper\", font_scale=1.2)\n",
"sns.despine(offset=10)\n",
"\n",
- "fig.savefig(plot_dir+'cc-error.pdf')"
+ "fig.savefig(plot_dir + \"cc-error.pdf\")"
]
},
{
@@ -732,59 +871,77 @@
"metadata": {},
"outputs": [],
"source": [
- "fig = plt.figure(figsize=(10,5))\n",
+ "fig = plt.figure(figsize=(10, 5))\n",
"\n",
- "cl_1 = (iapws._iapws._Liquid(265, 0.1)['cp'])*1000.\n",
- "cl_2 = (iapws._iapws._Liquid(305, 0.1)['cp'])*1000\n",
- "ci_1 = (iapws._iapws._Ice(193, 0.01)['cp'])*1000.\n",
- "ci_2 = (iapws._iapws._Ice(273, 0.10)['cp'])*1000\n",
+ "cl_1 = (iapws._iapws._Liquid(265, 0.1)[\"cp\"]) * 1000.0\n",
+ "cl_2 = (iapws._iapws._Liquid(305, 0.1)[\"cp\"]) * 1000\n",
+ "ci_1 = (iapws._iapws._Ice(193, 0.01)[\"cp\"]) * 1000.0\n",
+ "ci_2 = (iapws._iapws._Ice(273, 0.10)[\"cp\"]) * 1000\n",
"\n",
- "cls = np.arange(cl_2,cl_1)\n",
+ "cls = np.arange(cl_2, cl_1)\n",
"err = np.zeros(len(cls))\n",
"\n",
- "ax1 = plt.subplot(1,2,1)\n",
- "ax1.set_xlabel('$c_\\mathrm{liq}$ / Jkg$^{-1}$K$^{-1}$')\n",
- "ax1.set_ylabel('$(e_{\\mathrm{s,x}}/e_{\\mathrm{s,ref}} - 1)_\\mathrm{max}$ / %')\n",
- "ax1.set_yscale('log')\n",
- "\n",
- "state = 'liq'\n",
- "TK = np.arange(260,300,0.5)\n",
- "es_ref = es(TK,formula=\"wagner-pruss\",state=state)\n",
- "for i,cx in enumerate(cls):\n",
- " c1 = (cpv-cx)/Rv\n",
- " c2 = lvT/(Rv*TvT) - c1\n",
- " es_a = PvT * np.exp(c2*(1.-TvT/TK)) * (TK/TvT)**c1\n",
- " err[i] = np.max(np.abs(es_a/es_ref -1.))*100.\n",
- "ax1.plot(cls,err,c='tab:purple',ls='dotted',label='Analytic $c_\\mathrm{liq}$ for $T\\in$ (260K,305K)')\n",
- "ax1.legend(loc=\"upper left\",ncol=2)\n",
- "\n",
- "cis = np.arange(ci_1,ci_2)\n",
+ "ax1 = plt.subplot(1, 2, 1)\n",
+ "ax1.set_xlabel(\"$c_\\mathrm{liq}$ / Jkg$^{-1}$K$^{-1}$\")\n",
+ "ax1.set_ylabel(\"$(e_{\\mathrm{s,x}}/e_{\\mathrm{s,ref}} - 1)_\\mathrm{max}$ / %\")\n",
+ "ax1.set_yscale(\"log\")\n",
+ "\n",
+ "state = \"liq\"\n",
+ "TK = np.arange(260, 300, 0.5)\n",
+ "es_ref = es(TK, formula=\"wagner-pruss\", state=state)\n",
+ "for i, cx in enumerate(cls):\n",
+ " c1 = (cpv - cx) / Rv\n",
+ " c2 = lvT / (Rv * TvT) - c1\n",
+ " es_a = PvT * np.exp(c2 * (1.0 - TvT / TK)) * (TK / TvT) ** c1\n",
+ " err[i] = np.max(np.abs(es_a / es_ref - 1.0)) * 100.0\n",
+ "ax1.plot(\n",
+ " cls,\n",
+ " err,\n",
+ " c=\"tab:purple\",\n",
+ " ls=\"dotted\",\n",
+ " label=\"Analytic $c_\\mathrm{liq}$ for $T\\in$ (260K,305K)\",\n",
+ ")\n",
+ "ax1.legend(loc=\"upper left\", ncol=2)\n",
+ "\n",
+ "cis = np.arange(ci_1, ci_2)\n",
"err = np.zeros(len(cis))\n",
"\n",
- "ax2 = plt.subplot(1,2,2)\n",
- "ax2.set_xlabel('$c_\\mathrm{ice}$ / Jkg$^{-1}$K$^{-1}$')\n",
- "ax2.set_ylabel('$(e_{\\mathrm{s,x}}/e_{\\mathrm{s,ref}} - 1)_\\mathrm{max}$ / %')\n",
- "ax2.set_yscale('log')\n",
- "\n",
- "state = 'ice'\n",
- "TK = np.arange(180,273,0.5)\n",
- "es_ref = es(TK,formula=\"wagner-pruss\",state=state)\n",
- "for i,cx in enumerate(cis):\n",
- " c1 = (cpv-cx)/Rv\n",
- " c2 = lsT/(Rv*TvT) - c1\n",
- " es_a = PvT * np.exp(c2*(1.-TvT/TK)) * (TK/TvT)**c1\n",
- " err[i] = np.max(np.abs(es_a/es_ref -1.))*100.\n",
- "ax2.plot(cis,err,c='tab:purple',ls='dotted',label='Analytic $c_\\mathrm{ice}$ for $T\\in$ (193K,273K)')\n",
- "ax2.legend(loc=\"upper right\",ncol=2)\n",
+ "ax2 = plt.subplot(1, 2, 2)\n",
+ "ax2.set_xlabel(\"$c_\\mathrm{ice}$ / Jkg$^{-1}$K$^{-1}$\")\n",
+ "ax2.set_ylabel(\"$(e_{\\mathrm{s,x}}/e_{\\mathrm{s,ref}} - 1)_\\mathrm{max}$ / %\")\n",
+ "ax2.set_yscale(\"log\")\n",
+ "\n",
+ "state = \"ice\"\n",
+ "TK = np.arange(180, 273, 0.5)\n",
+ "es_ref = es(TK, formula=\"wagner-pruss\", state=state)\n",
+ "for i, cx in enumerate(cis):\n",
+ " c1 = (cpv - cx) / Rv\n",
+ " c2 = lsT / (Rv * TvT) - c1\n",
+ " es_a = PvT * np.exp(c2 * (1.0 - TvT / TK)) * (TK / TvT) ** c1\n",
+ " err[i] = np.max(np.abs(es_a / es_ref - 1.0)) * 100.0\n",
+ "ax2.plot(\n",
+ " cis,\n",
+ " err,\n",
+ " c=\"tab:purple\",\n",
+ " ls=\"dotted\",\n",
+ " label=\"Analytic $c_\\mathrm{ice}$ for $T\\in$ (193K,273K)\",\n",
+ ")\n",
+ "ax2.legend(loc=\"upper right\", ncol=2)\n",
"\n",
"sns.set_context(\"paper\", font_scale=1.2)\n",
"sns.despine(offset=10)\n",
"\n",
- "fig.savefig(plot_dir+'es-analytic-fits.pdf')\n",
+ "fig.savefig(plot_dir + \"es-analytic-fits.pdf\")\n",
"Tfit = 305\n",
- "print ('Taking fit for $c_\\mathrm{liq}=$ %3.2f J/(kg K) at $T=$ %3.2f K'%(iapws._iapws._Liquid(Tfit, 0.1)['cp']*1000.,Tfit))\n",
+ "print(\n",
+ " \"Taking fit for $c_\\mathrm{liq}=$ %3.2f J/(kg K) at $T=$ %3.2f K\"\n",
+ " % (iapws._iapws._Liquid(Tfit, 0.1)[\"cp\"] * 1000.0, Tfit)\n",
+ ")\n",
"Tfit = 247.065\n",
- "print ('Taking fit for $c_\\mathrm{ice}=$ %3.2f J/(kg K) at $T=$ %3.2f K'%(iapws._iapws._Ice(Tfit, 0.1)['cp']*1000.,Tfit))"
+ "print(\n",
+ " \"Taking fit for $c_\\mathrm{ice}=$ %3.2f J/(kg K) at $T=$ %3.2f K\"\n",
+ " % (iapws._iapws._Ice(Tfit, 0.1)[\"cp\"] * 1000.0, Tfit)\n",
+ ")"
]
},
{
@@ -802,67 +959,71 @@
"metadata": {},
"outputs": [],
"source": [
- "def rcemip_on_z(z,SST):\n",
+ "def rcemip_on_z(z, SST):\n",
" # function [T,q,p] = rcemip_on_z(z,SST)\n",
- " # \n",
+ " #\n",
" # Inputs:\n",
" # z: array of heights (low to high, m)\n",
" # SST: sea surface temperature (K)\n",
- " # \n",
+ " #\n",
" # Outputs:\n",
- " T = np.zeros(len(z)) # temperature (K)\n",
- " q = np.zeros(len(z)) # specific humidity (g/g)\n",
- " p = np.zeros(len(z)) # pressure (Pa)\n",
+ " T = np.zeros(len(z)) # temperature (K)\n",
+ " q = np.zeros(len(z)) # specific humidity (g/g)\n",
+ " p = np.zeros(len(z)) # pressure (Pa)\n",
"\n",
" ## Constants\n",
- " g = 9.79764 #m/s^2\n",
- " Rd = 287.04 #J/kgK\n",
- " \n",
+ " g = 9.79764 # m/s^2\n",
+ " Rd = 287.04 # J/kgK\n",
+ "\n",
" ## Parameters\n",
- " p0 = 101480 #Pa surface pressure\n",
- " qt = 10**(-11) #g/g specific humidity at tropopause\n",
- " zq1 = 4000 #m\n",
- " zq2 = 7500 #m\n",
- " zt = 15000 #m tropopause height\n",
- " gamma = 0.0067 #K/m lapse rate\n",
- " \n",
+ " p0 = 101480 # Pa surface pressure\n",
+ " qt = 10 ** (-11) # g/g specific humidity at tropopause\n",
+ " zq1 = 4000 # m\n",
+ " zq2 = 7500 # m\n",
+ " zt = 15000 # m tropopause height\n",
+ " gamma = 0.0067 # K/m lapse rate\n",
+ "\n",
" ## Scratch\n",
- " Tv = np.zeros(len(z)) # temperature (K)\n",
+ " Tv = np.zeros(len(z)) # temperature (K)\n",
"\n",
" if SST == 295:\n",
- " q0 = 0.01200; #g/g specific humidity at surface (adjusted from 300K value so RH near surface approx 80%)\n",
+ " q0 = 0.01200\n",
+ " # g/g specific humidity at surface (adjusted from 300K value so RH near surface approx 80%)\n",
" elif SST == 300:\n",
- " q0 = 0.01865; #g/g specific humidity at surface\n",
+ " q0 = 0.01865\n",
+ " # g/g specific humidity at surface\n",
" elif SST == 305:\n",
- " q0 = 0.02400 #g/g specific humidity at surface (adjusted from 300K value so RH near surface approx 80%)\n",
- " \n",
- " T0 = SST - 0 #surface air temperature adjusted to be 0K less than SST\n",
- " \n",
+ " q0 = 0.02400 # g/g specific humidity at surface (adjusted from 300K value so RH near surface approx 80%)\n",
+ "\n",
+ " T0 = SST - 0 # surface air temperature adjusted to be 0K less than SST\n",
+ "\n",
" ## Virtual Temperature at surface and tropopause\n",
- " Tv0 = T0*(1 + 0.608*q0) #virtual temperature at surface\n",
- " Tvt = Tv0 - gamma*zt #virtual temperature at tropopause z=zt\n",
- " \n",
+ " Tv0 = T0 * (1 + 0.608 * q0) # virtual temperature at surface\n",
+ " Tvt = Tv0 - gamma * zt # virtual temperature at tropopause z=zt\n",
+ "\n",
" ## Pressure\n",
- " pt = p0*(Tvt/Tv0)**(g/(Rd*gamma)); #pressure at tropopause z=zt\n",
- " p = p0*((Tv0-gamma*z)/Tv0)**(g/(Rd*gamma)) #0 <= z <= zt\n",
- " p[z>zt] = pt*np.exp(-g*(z[z>zt]-zt)/(Rd*Tvt)) #z > zt\n",
- " \n",
+ " pt = p0 * (Tvt / Tv0) ** (g / (Rd * gamma))\n",
+ " # pressure at tropopause z=zt\n",
+ " p = p0 * ((Tv0 - gamma * z) / Tv0) ** (g / (Rd * gamma)) # 0 <= z <= zt\n",
+ " p[z > zt] = pt * np.exp(-g * (z[z > zt] - zt) / (Rd * Tvt)) # z > zt\n",
+ "\n",
" ## Specific humidity\n",
- " q = q0*np.exp(-z/zq1)*np.exp(-(z/zq2)**2)\n",
- " q[z>zt] = qt #z > zt\n",
- " \n",
+ " q = q0 * np.exp(-z / zq1) * np.exp(-((z / zq2) ** 2))\n",
+ " q[z > zt] = qt # z > zt\n",
+ "\n",
" ## Temperature\n",
- " #Virtual Temperature\n",
- " Tv = Tv0 - gamma*z #0 <= z <= zt\n",
- " Tv[z>zt] = Tvt #z > zt\n",
- " \n",
- " #Absolute Temperature at all heights\n",
- " T = Tv/(1 + 0.608*q)\n",
- " \n",
+ " # Virtual Temperature\n",
+ " Tv = Tv0 - gamma * z # 0 <= z <= zt\n",
+ " Tv[z > zt] = Tvt # z > zt\n",
+ "\n",
+ " # Absolute Temperature at all heights\n",
+ " T = Tv / (1 + 0.608 * q)\n",
+ "\n",
" return T, q, p\n",
"\n",
- "z = np.arange(0,17000,100)\n",
- "T, q , p = rcemip_on_z(z,300)"
+ "\n",
+ "z = np.arange(0, 17000, 100)\n",
+ "T, q, p = rcemip_on_z(z, 300)"
]
},
{
@@ -871,33 +1032,38 @@
"metadata": {},
"outputs": [],
"source": [
- "def get_rh (T,q,p,formula='wagner-pruss',state='liq'):\n",
- " es_w = es(T,formula=formula,state=state)\n",
- " x = es_w * eps1/(p-es_w)\n",
- " return 100.*q*(1+x)/x\n",
- " \n",
- "fig = plt.figure(figsize=(4,5))\n",
- "\n",
- "ax1 = plt.subplot(1,1,1)\n",
- "ax1.set_ylabel('$z$ / km')\n",
- "ax1.set_xlabel('RH / %')\n",
- "ax1.set_ylim(0,14.5)\n",
- "ax1.set_yticks([0,4,8,12])\n",
- "\n",
- "plt.plot(get_rh(T,q,p,state='mxd'),z/1000.,label = 'Wagner Pruss (ice/liq)')\n",
- "plt.plot(get_rh(T+1,q,p,state='mxd'),z/1000.,label = 'Wagner Pruss (ice/liq) + 1 K')\n",
- "plt.plot(get_rh(T,q,p,state='ice'),z/1000.,label = 'Wagner Pruss (ice)')\n",
- "plt.plot(get_rh(T,q,p,formula='romps',state='mxd'),z/1000.,label = 'Romps (ice/liq)')\n",
- "plt.plot(get_rh(T,q,p),z/1000.,label = 'Wagner Pruss (liq)')\n",
- "plt.plot(get_rh(T,q,p,formula='flatau'),z/1000.,label = 'Flatau (liq)')\n",
- "\n",
- "plt.legend(loc=\"lower left\",ncol=1)\n",
+ "def get_rh(T, q, p, formula=\"wagner-pruss\", state=\"liq\"):\n",
+ " es_w = es(T, formula=formula, state=state)\n",
+ " x = es_w * eps1 / (p - es_w)\n",
+ " return 100.0 * q * (1 + x) / x\n",
+ "\n",
+ "\n",
+ "fig = plt.figure(figsize=(4, 5))\n",
+ "\n",
+ "ax1 = plt.subplot(1, 1, 1)\n",
+ "ax1.set_ylabel(\"$z$ / km\")\n",
+ "ax1.set_xlabel(\"RH / %\")\n",
+ "ax1.set_ylim(0, 14.5)\n",
+ "ax1.set_yticks([0, 4, 8, 12])\n",
+ "\n",
+ "plt.plot(get_rh(T, q, p, state=\"mxd\"), z / 1000.0, label=\"Wagner Pruss (ice/liq)\")\n",
+ "plt.plot(\n",
+ " get_rh(T + 1, q, p, state=\"mxd\"), z / 1000.0, label=\"Wagner Pruss (ice/liq) + 1 K\"\n",
+ ")\n",
+ "plt.plot(get_rh(T, q, p, state=\"ice\"), z / 1000.0, label=\"Wagner Pruss (ice)\")\n",
+ "plt.plot(\n",
+ " get_rh(T, q, p, formula=\"romps\", state=\"mxd\"), z / 1000.0, label=\"Romps (ice/liq)\"\n",
+ ")\n",
+ "plt.plot(get_rh(T, q, p), z / 1000.0, label=\"Wagner Pruss (liq)\")\n",
+ "plt.plot(get_rh(T, q, p, formula=\"flatau\"), z / 1000.0, label=\"Flatau (liq)\")\n",
+ "\n",
+ "plt.legend(loc=\"lower left\", ncol=1)\n",
"\n",
"sns.set_context(\"paper\")\n",
"sns.despine(offset=10)\n",
"plt.tight_layout()\n",
"\n",
- "fig.savefig(plot_dir+'RCEMIP-RHerror.pdf')"
+ "fig.savefig(plot_dir + \"RCEMIP-RHerror.pdf\")"
]
},
{
@@ -918,9 +1084,9 @@
"outputs": [],
"source": [
"# Version 1.0 released by David Romps on September 12, 2017.\n",
- "# \n",
+ "#\n",
"# When using this code, please cite:\n",
- "# \n",
+ "#\n",
"# @article{16lcl,\n",
"# Title = {Exact expression for the lifting condensation level},\n",
"# Author = {David M. Romps},\n",
@@ -936,46 +1102,56 @@
"# - Exactly one of rh, rhl, and rhs (dimensionless, from 0 to 1):\n",
"# * The value of rh is interpreted to be the relative humidity with\n",
"# respect to liquid water if T >= 273.15 K and with respect to ice if\n",
- "# T < 273.15 K. \n",
+ "# T < 273.15 K.\n",
"# * The value of rhl is interpreted to be the relative humidity with\n",
"# respect to liquid water\n",
"# * The value of rhs is interpreted to be the relative humidity with\n",
"# respect to ice\n",
"# - ldl is an optional logical flag. If true, the lifting deposition\n",
- "# level (LDL) is returned instead of the LCL. \n",
+ "# level (LDL) is returned instead of the LCL.\n",
"# - min_lcl_ldl is an optional logical flag. If true, the minimum of the\n",
"# LCL and LDL is returned.\n",
"\n",
- "def lcl(p,T,rh=None,rhl=None,rhs=None,return_ldl=False,return_min_lcl_ldl=False):\n",
+ "\n",
+ "def lcl(p, T, rh=None, rhl=None, rhs=None, return_ldl=False, return_min_lcl_ldl=False):\n",
"\n",
" import math\n",
" import scipy.special\n",
"\n",
" # Parameters\n",
- " Ttrip = 273.16 # K\n",
- " ptrip = 611.65 # Pa\n",
- " E0v = 2.3740e6 # J/kg\n",
- " E0s = 0.3337e6 # J/kg\n",
- " ggr = 9.81 # m/s^2\n",
- " rgasa = 287.04 # J/kg/K \n",
- " rgasv = 461 # J/kg/K \n",
- " cva = 719 # J/kg/K\n",
- " cvv = 1418 # J/kg/K \n",
- " cvl = 4119 # J/kg/K \n",
- " cvs = 1861 # J/kg/K \n",
- " cpa = cva + rgasa\n",
- " cpv = cvv + rgasv\n",
+ " Ttrip = 273.16 # K\n",
+ " ptrip = 611.65 # Pa\n",
+ " E0v = 2.3740e6 # J/kg\n",
+ " E0s = 0.3337e6 # J/kg\n",
+ " ggr = 9.81 # m/s^2\n",
+ " rgasa = 287.04 # J/kg/K\n",
+ " rgasv = 461 # J/kg/K\n",
+ " cva = 719 # J/kg/K\n",
+ " cvv = 1418 # J/kg/K\n",
+ " cvl = 4119 # J/kg/K\n",
+ " cvs = 1861 # J/kg/K\n",
+ " cpa = cva + rgasa\n",
+ " cpv = cvv + rgasv\n",
"\n",
" # The saturation vapor pressure over liquid water\n",
" def pvstarl(T):\n",
- " return ptrip * (T/Ttrip)**((cpv-cvl)/rgasv) * math.exp( (E0v - (cvv-cvl)*Ttrip) / rgasv * (1/Ttrip - 1/T) )\n",
+ " return (\n",
+ " ptrip\n",
+ " * (T / Ttrip) ** ((cpv - cvl) / rgasv)\n",
+ " * math.exp((E0v - (cvv - cvl) * Ttrip) / rgasv * (1 / Ttrip - 1 / T))\n",
+ " )\n",
+ "\n",
" # The saturation vapor pressure over solid ice\n",
" def pvstars(T):\n",
- " return ptrip * (T/Ttrip)**((cpv-cvs)/rgasv) * math.exp( (E0v + E0s - (cvv-cvs)*Ttrip) / rgasv * (1/Ttrip - 1/T)) \n",
+ " return (\n",
+ " ptrip\n",
+ " * (T / Ttrip) ** ((cpv - cvs) / rgasv)\n",
+ " * math.exp((E0v + E0s - (cvv - cvs) * Ttrip) / rgasv * (1 / Ttrip - 1 / T))\n",
+ " )\n",
"\n",
" # Calculate pv from rh, rhl, or rhs\n",
" rh_counter = 0\n",
- " if rh is not None:\n",
+ " if rh is not None:\n",
" rh_counter = rh_counter + 1\n",
" if rhl is not None:\n",
" rh_counter = rh_counter + 1\n",
@@ -983,11 +1159,11 @@
" rh_counter = rh_counter + 1\n",
" if rh_counter != 1:\n",
" print(rh_counter)\n",
- " exit('Error in lcl: Exactly one of rh, rhl, and rhs must be specified')\n",
+ " exit(\"Error in lcl: Exactly one of rh, rhl, and rhs must be specified\")\n",
" if rh is not None:\n",
- " # The variable rh is assumed to be \n",
- " # with respect to liquid if T > Ttrip and \n",
- " # with respect to solid if T < Ttrip\n",
+ " # The variable rh is assumed to be\n",
+ " # with respect to liquid if T > Ttrip and\n",
+ " # with respect to solid if T < Ttrip\n",
" if T > Ttrip:\n",
" pv = rh * pvstarl(T)\n",
" else:\n",
@@ -1011,34 +1187,34 @@
" if pv > p:\n",
" return N\n",
"\n",
- "# Calculate lcl_liquid and lcl_solid\n",
- " qv = rgasa*pv / (rgasv*p + (rgasa-rgasv)*pv)\n",
- " rgasm = (1-qv)*rgasa + qv*rgasv\n",
- " cpm = (1-qv)*cpa + qv*cpv\n",
+ " # Calculate lcl_liquid and lcl_solid\n",
+ " qv = rgasa * pv / (rgasv * p + (rgasa - rgasv) * pv)\n",
+ " rgasm = (1 - qv) * rgasa + qv * rgasv\n",
+ " cpm = (1 - qv) * cpa + qv * cpv\n",
" if rh == 0:\n",
- " return cpm*T/ggr\n",
- " aL = -(cpv-cvl)/rgasv + cpm/rgasm\n",
- " bL = -(E0v-(cvv-cvl)*Ttrip)/(rgasv*T)\n",
- " cL = pv/pvstarl(T)*math.exp(-(E0v-(cvv-cvl)*Ttrip)/(rgasv*T))\n",
- " aS = -(cpv-cvs)/rgasv + cpm/rgasm\n",
- " bS = -(E0v+E0s-(cvv-cvs)*Ttrip)/(rgasv*T)\n",
- " cS = pv/pvstars(T)*math.exp(-(E0v+E0s-(cvv-cvs)*Ttrip)/(rgasv*T))\n",
- " X = bL/(aL*scipy.special.lambertw(bL/aL*cL**(1/aL),-1).real)\n",
- " Y = bS/(aS*scipy.special.lambertw(bS/aS*cS**(1/aS),-1).real) \n",
- " \n",
- " lcl = cpm*T/ggr*( 1 - X)\n",
- " ldl = cpm*T/ggr*( 1 - Y)\n",
+ " return cpm * T / ggr\n",
+ " aL = -(cpv - cvl) / rgasv + cpm / rgasm\n",
+ " bL = -(E0v - (cvv - cvl) * Ttrip) / (rgasv * T)\n",
+ " cL = pv / pvstarl(T) * math.exp(-(E0v - (cvv - cvl) * Ttrip) / (rgasv * T))\n",
+ " aS = -(cpv - cvs) / rgasv + cpm / rgasm\n",
+ " bS = -(E0v + E0s - (cvv - cvs) * Ttrip) / (rgasv * T)\n",
+ " cS = pv / pvstars(T) * math.exp(-(E0v + E0s - (cvv - cvs) * Ttrip) / (rgasv * T))\n",
+ " X = bL / (aL * scipy.special.lambertw(bL / aL * cL ** (1 / aL), -1).real)\n",
+ " Y = bS / (aS * scipy.special.lambertw(bS / aS * cS ** (1 / aS), -1).real)\n",
+ "\n",
+ " lcl = cpm * T / ggr * (1 - X)\n",
+ " ldl = cpm * T / ggr * (1 - Y)\n",
"\n",
" # Modifications of the code to output Plcl or Pldl\n",
- " Plcl = PPa * X**(cpm/rgasm)\n",
- " Pldl = PPa * X**(cpm/rgasm)\n",
+ " Plcl = PPa * X ** (cpm / rgasm)\n",
+ " Pldl = PPa * X ** (cpm / rgasm)\n",
" # Return either lcl or ldl\n",
" if return_ldl and return_min_lcl_ldl:\n",
- " exit('return_ldl and return_min_lcl_ldl cannot both be true')\n",
+ " exit(\"return_ldl and return_min_lcl_ldl cannot both be true\")\n",
" elif return_ldl:\n",
" return Pldl\n",
" elif return_min_lcl_ldl:\n",
- " return min(Plcl,Pldl)\n",
+ " return min(Plcl, Pldl)\n",
" else:\n",
" return Plcl"
]
@@ -1050,60 +1226,63 @@
"outputs": [],
"source": [
"import aes_thermo as mt\n",
- "PPa = 101325.\n",
"\n",
- "qt = np.arange(2.5e-3,8e-3,0.2e-3)\n",
- "TK = 285.\n",
- "Plcl_X = mt.plcl(TK,PPa,qt)\n",
- "Plcl_B = mt.plcl_boloton(TK,PPa,qt)\n",
+ "PPa = 101325.0\n",
+ "\n",
+ "qt = np.arange(2.5e-3, 8e-3, 0.2e-3)\n",
+ "TK = 285.0\n",
+ "Plcl_X = mt.plcl(TK, PPa, qt)\n",
+ "Plcl_B = mt.plcl_boloton(TK, PPa, qt)\n",
"Plcl_R = np.zeros(len(Plcl_X))\n",
"\n",
- "for i,x in enumerate(qt):\n",
- " if (x>0.1): x = x/1000.\n",
- " RH = mt.mr2pp(x/(1.-x),PPa)/mt.es(TK)\n",
- " Plcl_R[i] = lcl(PPa,TK,RH)\n",
+ "for i, x in enumerate(qt):\n",
+ " if x > 0.1:\n",
+ " x = x / 1000.0\n",
+ " RH = mt.mr2pp(x / (1.0 - x), PPa) / mt.es(TK)\n",
+ " Plcl_R[i] = lcl(PPa, TK, RH)\n",
"\n",
- "del1 = (Plcl_B-Plcl_X)/100.\n",
- "del2 = (Plcl_R-Plcl_X)/100.\n",
+ "del1 = (Plcl_B - Plcl_X) / 100.0\n",
+ "del2 = (Plcl_R - Plcl_X) / 100.0\n",
"\n",
- "fig = plt.figure(figsize=(10,5))\n",
- "ax1 = plt.subplot(1,2,1)\n",
- "ax1.set_ylabel('$P$ / hPa')\n",
- "ax1.set_xlabel('$q_\\mathrm{t}$ / g/kg')\n",
- "#ax1.set_ylim(-1.2,1.2)\n",
+ "fig = plt.figure(figsize=(10, 5))\n",
+ "ax1 = plt.subplot(1, 2, 1)\n",
+ "ax1.set_ylabel(\"$P$ / hPa\")\n",
+ "ax1.set_xlabel(\"$q_\\mathrm{t}$ / g/kg\")\n",
+ "# ax1.set_ylim(-1.2,1.2)\n",
"\n",
- "plt.plot(qt*1.e3,del1,label='$\\\\delta_\\mathrm{B}$, $T$=285K')\n",
- "plt.plot(qt*1.e3,del2,label='$\\\\delta_\\mathrm{R}$, $T$=285K')\n",
- "#plt.gca().invert_yaxis()\n",
+ "plt.plot(qt * 1.0e3, del1, label=\"$\\\\delta_\\mathrm{B}$, $T$=285K\")\n",
+ "plt.plot(qt * 1.0e3, del2, label=\"$\\\\delta_\\mathrm{R}$, $T$=285K\")\n",
+ "# plt.gca().invert_yaxis()\n",
"plt.legend(loc=\"best\")\n",
"\n",
- "qt = np.arange(0.5e-3,28e-3,0.2e-3)\n",
- "TK = 310.\n",
- "Plcl_X = mt.get_Plcl(TK,PPa,qt,iterate=True)\n",
- "Plcl_B = mt.get_Plcl(TK,PPa,qt)\n",
+ "qt = np.arange(0.5e-3, 28e-3, 0.2e-3)\n",
+ "TK = 310.0\n",
+ "Plcl_X = mt.get_Plcl(TK, PPa, qt, iterate=True)\n",
+ "Plcl_B = mt.get_Plcl(TK, PPa, qt)\n",
"Plcl_R = np.zeros(len(Plcl_X))\n",
"\n",
- "for i,x in enumerate(qt):\n",
- " if (x>0.1): x = x/1000.\n",
- " RH = mt.mr2pp(x/(1.-x),PPa)/mt.es(TK)\n",
- " Plcl_R[i] = lcl(PPa,TK,RH)\n",
+ "for i, x in enumerate(qt):\n",
+ " if x > 0.1:\n",
+ " x = x / 1000.0\n",
+ " RH = mt.mr2pp(x / (1.0 - x), PPa) / mt.es(TK)\n",
+ " Plcl_R[i] = lcl(PPa, TK, RH)\n",
"\n",
- "del1 = (Plcl_B-Plcl_X)/100.\n",
- "del2 = (Plcl_R-Plcl_X)/100.\n",
+ "del1 = (Plcl_B - Plcl_X) / 100.0\n",
+ "del2 = (Plcl_R - Plcl_X) / 100.0\n",
"\n",
- "ax2 = plt.subplot(1,2,2)\n",
- "ax2.set_xlabel('$q_\\mathrm{t}$ / g/kg')\n",
- "#ax2.set_ylim(-1.2,1.2)\n",
+ "ax2 = plt.subplot(1, 2, 2)\n",
+ "ax2.set_xlabel(\"$q_\\mathrm{t}$ / g/kg\")\n",
+ "# ax2.set_ylim(-1.2,1.2)\n",
"ax2.set_yticklabels([])\n",
"\n",
- "plt.plot(qt*1.e3,del1,label='$\\\\delta_\\mathrm{B}$, $T$=310K')\n",
- "plt.plot(qt*1.e3,del2,label='$\\\\delta_\\mathrm{R}$, $T$=310K')\n",
- "#plt.gca().invert_yaxis()\n",
+ "plt.plot(qt * 1.0e3, del1, label=\"$\\\\delta_\\mathrm{B}$, $T$=310K\")\n",
+ "plt.plot(qt * 1.0e3, del2, label=\"$\\\\delta_\\mathrm{R}$, $T$=310K\")\n",
+ "# plt.gca().invert_yaxis()\n",
"plt.legend(loc=\"best\")\n",
"\n",
"sns.set_context(\"talk\", font_scale=1.2)\n",
"sns.despine(offset=10)\n",
- "fig.savefig(plot_dir+'Plcl.pdf')"
+ "fig.savefig(plot_dir + \"Plcl.pdf\")"
]
},
{
diff --git a/moist_thermodynamics/data/cp-ice-vap.dat b/moist_thermodynamics/data/cp-ice-vap.dat
deleted file mode 100644
index 755e4224e2c22c2cb55c2f0f8b73e3afbc150673..0000000000000000000000000000000000000000
--- a/moist_thermodynamics/data/cp-ice-vap.dat
+++ /dev/null
@@ -1,620 +0,0 @@
- 0.18031000000E+03 0.92811184342E+03 0.68699428861E-07 0.14316725673E+04 0.18504422737E+04 0.28262467370E+07
- 0.18046000000E+03 0.92809772771E+03 0.70607736279E-07 0.14327030300E+04 0.18504470336E+04 0.28263094726E+07
- 0.18061000000E+03 0.92808359538E+03 0.72565744639E-07 0.14337336577E+04 0.18504518079E+04 0.28263720543E+07
- 0.18076000000E+03 0.92806944644E+03 0.74574659591E-07 0.14347644503E+04 0.18504565966E+04 0.28264344820E+07
- 0.18091000000E+03 0.92805528090E+03 0.76635713801E-07 0.14357954082E+04 0.18504613998E+04 0.28264967558E+07
- 0.18106000000E+03 0.92804109877E+03 0.78750167500E-07 0.14368265313E+04 0.18504662175E+04 0.28265588755E+07
- 0.18121000000E+03 0.92802690007E+03 0.80919309050E-07 0.14378578200E+04 0.18504710498E+04 0.28266208413E+07
- 0.18136000000E+03 0.92801268480E+03 0.83144455516E-07 0.14388892744E+04 0.18504758967E+04 0.28266826530E+07
- 0.18151000000E+03 0.92799845300E+03 0.85426953248E-07 0.14399208946E+04 0.18504807584E+04 0.28267443107E+07
- 0.18166000000E+03 0.92798420466E+03 0.87768178482E-07 0.14409526808E+04 0.18504856348E+04 0.28268058142E+07
- 0.18181000000E+03 0.92796993980E+03 0.90169537937E-07 0.14419846331E+04 0.18504905261E+04 0.28268671637E+07
- 0.18196000000E+03 0.92795565844E+03 0.92632469441E-07 0.14430167517E+04 0.18504954322E+04 0.28269283590E+07
- 0.18211000000E+03 0.92794136059E+03 0.95158442550E-07 0.14440490366E+04 0.18505003534E+04 0.28269894001E+07
- 0.18226000000E+03 0.92792704627E+03 0.97748959193E-07 0.14450814881E+04 0.18505052895E+04 0.28270502871E+07
- 0.18241000000E+03 0.92791271548E+03 0.10040555432E-06 0.14461141062E+04 0.18505102407E+04 0.28271110199E+07
- 0.18256000000E+03 0.92789836824E+03 0.10312979657E-06 0.14471468912E+04 0.18505152071E+04 0.28271715984E+07
- 0.18271000000E+03 0.92788400456E+03 0.10592328893E-06 0.14481798430E+04 0.18505201887E+04 0.28272320227E+07
- 0.18286000000E+03 0.92786962446E+03 0.10878766944E-06 0.14492129619E+04 0.18505251855E+04 0.28272922927E+07
- 0.18301000000E+03 0.92785522796E+03 0.11172461189E-06 0.14502462479E+04 0.18505301977E+04 0.28273524085E+07
- 0.18316000000E+03 0.92784081506E+03 0.11473582652E-06 0.14512797011E+04 0.18505352253E+04 0.28274123698E+07
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diff --git a/moist_thermodynamics/data/cp-liq-vap.dat b/moist_thermodynamics/data/cp-liq-vap.dat
deleted file mode 100644
index 312b14deac10f7317dd0d7b2a18055bcbbcca6b9..0000000000000000000000000000000000000000
--- a/moist_thermodynamics/data/cp-liq-vap.dat
+++ /dev/null
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diff --git a/moist_thermodynamics/data/psat.dat b/moist_thermodynamics/data/psat.dat
deleted file mode 100644
index 4924bfebcb82c9b379e5e891482a7c875c323b4a..0000000000000000000000000000000000000000
--- a/moist_thermodynamics/data/psat.dat
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diff --git a/moist_thermodynamics/plots/RCEMIP-RHerror.pdf b/moist_thermodynamics/plots/RCEMIP-RHerror.pdf
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diff --git a/moist_thermodynamics/plots/es-analytic-fits.pdf b/moist_thermodynamics/plots/es-analytic-fits.pdf
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diff --git a/moist_thermodynamics/plots/es_lsc-error.pdf b/moist_thermodynamics/plots/es_lsc-error.pdf
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diff --git a/moist_thermodynamics/saturation_vapor_pressures.py b/moist_thermodynamics/saturation_vapor_pressures.py
index c89710a64dde48501ec9e508d5d4ed680425f9cc..8156d3d70e6a93c6bb8da1b31e9cef3fbc247360 100644
--- a/moist_thermodynamics/saturation_vapor_pressures.py
+++ b/moist_thermodynamics/saturation_vapor_pressures.py
@@ -142,20 +142,19 @@ def liq_hardy(T):
return np.exp(X)
-def analytic(T, lx, cx):
- """returns saturation vapor pressure over a given phase
+def make_analytic(lx, cx):
+ """closure function for analytic saturation vapor pressure
- Uses the rankine (constant specific heat, negligible condensate volume) approximations to
+ Sets up the rankine (constant specific heat, negligible condensate volume) approximations to
calculate the saturation vapor pressure over a phase with the specific heat cx, and phase
change enthalpy (from vapor) lx, at temperature T.
Args:
- T: temperature in kelvin
lx: phase change enthalpy between vapor and given phase (liquid, ice)
cx: specific heat capacity of given phase (liquid, ice)
Returns:
- value of saturation vapor pressure over liquid water in Pa
+ a function for the saturation vaporp pressure consistent with choice of lx and cx
Reference:
Romps, D. M. Exact Expression for the Lifting Condensation Level. Journal of the Atmospheric
@@ -163,139 +162,79 @@ def analytic(T, lx, cx):
Romps, D. M. Accurate expressions for the dew point and frost point derived from the Rankine-
Kirchhoff approximations. Journal of the Atmospheric Sciences (2021) doi:10.1175/JAS-D-20-0301.1.
- >>> analytic(305.,constants.lvT,constants.cl)
- 4711.131611687174
+ >>> es = make_analytic(constants.lvT,constants.cl)
+ >>> es( np.asarray([273.15,260.]) )
+ array([611.21094488, 222.70984761])
"""
- TvT = constants.temperature_water_vapor_triple_point
- PvT = constants.pressure_water_vapor_triple_point
- Rv = constants.water_vapor_gas_constant
- c1 = (constants.cpv - cx) / Rv
- c2 = lx / (Rv * TvT) - c1
- es = PvT * np.exp(c2 * (1.0 - TvT / T)) * (T / TvT) ** c1
- return es
+ def es(T):
+ """Returns satruation vapor pressure (Pa) over liquid constructed using analytic expression
+ This function is constructed from the make_analytic closure and returns the saturation vapor
+ pressure defined by the phase change enthalpy and specific heat used in the closure. See
+ make_analytic
-def liq_analytic(T, lx=constants.lvT, cx=constants.cl):
- """Analytic approximation for saturation vapor pressure over iquid
+ Args:
+ T: temperature in kelvin
+ """
- Uses the rankine (constant specific heat, negligible condensate volume) approximations to
- calculate the saturation vapor pressure over liquid. The procedure is described in Eq(4) of
- Romps (2017) and best approximates the actual value for specific heats that differ slightly
- from the best estimates of these quantities which are provided as default quantities.
- Romps recommends cl = 4119 J/kg/K, and cpv = 1861 J/kg/K.
+ TvT = constants.temperature_water_vapor_triple_point
+ PvT = constants.pressure_water_vapor_triple_point
+ Rv = constants.water_vapor_gas_constant
- Args:
- T: temperature in kelvin
- lx: enthalpy of vaporization, at triple point, default constants.lvT
- cl: specific heat capacity of liquid at triple point
+ c1 = (constants.cpv - cx) / Rv
+ c2 = lx / (Rv * TvT) - c1
+ return PvT * np.exp(c2 * (1.0 - TvT / T)) * (T / TvT) ** c1
- Returns:
- value of saturation vapor pressure over liquid water in Pa
+ return es
- Reference:
- Romps, D. M. Exact Expression for the Lifting Condensation Level. Journal of the Atmospheric
- Sciences 74, 3891–3900 (2017).
- Romps, D. M. Accurate expressions for the dew point and frost point derived from the Rankine-
- Kirchhoff approximations. Journal of the Atmospheric Sciences (2021) doi:10.1175/JAS-D-20-0301.1.
- >>> liq_analytic(np.asarray([273.16,305.]))
- array([ 611.655 , 4711.13161169])
- """
- return analytic(T, lx, cx)
+liq_analytic = make_analytic(lx=constants.lvT, cx=constants.cl)
+ice_analytic = make_analytic(lx=constants.lsT, cx=constants.ci)
-def ice_analytic(T, lx=constants.lsT, cx=constants.ci):
- """Analytic approximation for saturation vapor pressure over ice
+def make_tetens(Tref, Pref, a, b):
+ """closure function for tetens saturation vapor pressure
- Uses the rankine (constant specific heat, negligible condensate volume) approximations to
- calculate the saturation vapor pressure over ice. The procedure is described in Eq(4) of
- Romps (2017) and best approximates the actual value for specific heats that differ slightly
- from the best estimates of these quantities which are provided as default quantities.
- Romps recommends ci = 1861 J/kg/K, and cpv = 1879 J/kg/K.
+ Constructs the teten's function for the moist static energy through the specification of the
+ constants a and b. As such a Teten's formula can specified for either ice or water, or adapted
+ as originally impelemented in ICON, in which case PvT and TvT need to be substituted by Pv0 and T0.
Args:
- T: temperature in kelvin
- lx: enthalpy of sublimation, at triple point, default constants.lsT
- ci: specific heat capacity of ice Ih, at triple point
+ Tref: reference temperature in kelvin
+ Pref: reference saturation vapor pressure in hPa
+ a: fitting parameter
+ b: fitting parameter
Returns:
- value of saturation vapor pressure over ice in Pa
-
- Reference:
- Romps, D. M. Exact Expression for the Lifting Condensation Level. Journal of the Atmospheric
- Sciences 74, 3891–3900 (2017).
- Romps, D. M. Accurate expressions for the dew point and frost point derived from the Rankine-
- Kirchhoff approximations. Journal of the Atmospheric Sciences (2021) doi:10.1175/JAS-D-20-0301.1.
-
-
- >>> ice_analytic(np.asarray([273.16,260.]))
- array([611.655 , 195.99959431])
- """
- return analytic(T, lx, cx)
-
-
-def tetens(T, a, b):
- """Returns saturation vapor pressure over liquid using the Magnus-Teten's formula
-
- This equation is written in a general form, with the constants a and b determining the fit. As
- such it can be specified for either ice or water, or adapted as originally impelemented in ICON,
- in which case PvT and TvT need to be substituted by Pv0 and T0.
-
- Args:
- T: temperature in kelvin
-
- >>> tetens(285.,17.269,35.86)
- 1389.7114123472836
- """
-
- es = constants.PvT * np.exp(a * (T - constants.TvT) / (T - b))
- return es
-
-
-def liq_tetens(T):
- """Returns saturation vapor pressure over liquid using the Magnus-Teten's formula
-
- This equation is what is used in the ICON code, hence its inclusion in this library. The original
- ICON implementation followed Murray's choice of constants (T0=273.15, Pv0=610.78, a=17.269, b=35.86).
- This implementation is referenced to the triple point values of temperature and vapor and with
- revised constants (a,b) chosen to better agree with the fits of Wagner and Pruss
-
- Args:
- T: temperature in kelvin
+ Murray's form of the Teten formula given the parameters
Reference:
Murray, F. W. On the Computation of Saturation Vapor Pressure. Journal of Applied Meteorology
and Climatology 6, 203–204 (1967).
- >>> liq_tetens(np.asarray([273.16,305.]))
- array([ 611.655 , 4719.73680592])
+ >>> es = make_tetens(Tref=constants.TvT, Pref=constants.PvT, a=22.0420, b=5.0)
+ >>> es( np.asarray([273.15,260.]) )
+ array([611.15242458, 196.1007033 ])
"""
- a = 17.41463775
- b = 33.6393413
- return tetens(T, a, b)
+ def es(T):
+ """Returns satruation vapor pressure (Pa) over liquid constructed using Teten's expression
+ This function is constructed from the make_tetens closure and returns the saturation vapor
+ pressure defined by the refrence state and parameters of that fit See make_analytic
-def ice_tetens(T):
- """Returns saturation vapor pressure over liquid using the Magnus-Teten's formula
+ Args:
+ T: temperature in kelvin
+ """
- This equation is what is used in the ICON code, hence its inclusion in this library. The original
- ICON implementation followed Murray's choice of constants (T0=273.15, Pv0=610.78, a=21.875, b=7.66).
- This implementation is referenced to the triple point values of temperature and vapor and with
- revised constants (a,b) chosen to better agree with the fits of Wagner and Pruss
+ return Pref * np.exp(a * (T - Tref) / (T - b))
- Args:
- T: temperature in kelvin
+ return es
- Reference:
- Murray, F. W. On the Computation of Saturation Vapor Pressure. Journal of Applied Meteorology
- and Climatology 6, 203–204 (1967).
- >>> ice_tetens(np.asarray([273.16,260.]))
- array([611.655 , 196.10072658])
- """
- a = 22.0419977
- b = 5.0
+liq_tetens = make_tetens(Tref=constants.TvT, Pref=constants.PvT, a=17.4146, b=33.639)
+ice_tetens = make_tetens(Tref=constants.TvT, Pref=constants.PvT, a=22.0420, b=5.0)
+es_default = make_analytic(lx=constants.lv0, cx=constants.cl)
- return tetens(T, a, b)
+es = es_default