From 2b9cf304ee2760db9ad71790c3dc804066c877e1 Mon Sep 17 00:00:00 2001
From: bjorn-stevens <64255981+bjorn-stevens@users.noreply.github.com>
Date: Fri, 12 Aug 2022 19:13:47 +0200
Subject: [PATCH] added moist adiabat and theta to functions

I added the calculation of the moist adiabat from the integration of the
first law to the functions, and a generalized definition of the 'dry'
potential temperature, which can account for moisture effects on
thermodynamic parameters.

An additional example was added to show the added functionality.
---
 examples/examples.ipynb           | 139 ++++++++++++++++++++++++++++--
 moist_thermodynamics/functions.py |  97 +++++++++++++++++++++
 2 files changed, 230 insertions(+), 6 deletions(-)

diff --git a/examples/examples.ipynb b/examples/examples.ipynb
index 6d955cd..9b28f1c 100644
--- a/examples/examples.ipynb
+++ b/examples/examples.ipynb
@@ -27,6 +27,7 @@
     "1. constructing a moist adiabat.\n",
     "2. sensitivity of moist adiabat to saturation vapor pressure \n",
     "3. lcl computations\n",
+    "4. Integrating the first law to arrive at the moist adiabat\n",
     "\n",
     "## 1. Constructing a moist adiabat\n",
     "\n",
@@ -35,13 +36,41 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 2,
+   "id": "a82ec75a-a480-40c2-bb07-6c73a2a745e5",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([611.65715494, 222.65143353])"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "mt.es_liq_hardy(np.asarray([273.16,260.]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
    "id": "0f765565-ed26-4cc7-a859-bebf9b020aea",
    "metadata": {},
    "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.016751645341371288\n"
+     ]
+    },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 504x360 with 1 Axes>"
       ]
@@ -53,7 +82,7 @@
     }
    ],
    "source": [
-    "es      = mt.es_liq\n",
+    "es      = mt.es_liq_analytic\n",
     "p2q     = mt.partial_pressure_to_specific_humidity\n",
     "theta_l = mt.theta_l\n",
     "Tl2T    = np.vectorize(mt.T_from_Tl)\n",
@@ -66,6 +95,7 @@
     "\n",
     "RH   = 0.77\n",
     "qt   = p2q(RH*es(Tsfc),Psfc)\n",
+    "print (qt)\n",
     "\n",
     "sns.set_context('talk')\n",
     "fig, ax = plt.subplots(figsize = (7,5), constrained_layout = True)\n",
@@ -99,7 +129,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 4,
    "id": "321bddff-0bb6-4b3a-a3f0-1dae1c50c852",
    "metadata": {},
    "outputs": [
@@ -170,7 +200,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 5,
    "id": "a53539ae-7920-41b9-aa41-fed0031ce16b",
    "metadata": {},
    "outputs": [],
@@ -303,7 +333,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 6,
    "id": "9b2830db-855d-467d-ac66-cc9154ab7caa",
    "metadata": {},
    "outputs": [
@@ -379,6 +409,103 @@
     "sns.despine(offset=10)\n",
     "#fig.savefig(plot_dir+'Plcl.pdf')"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cb6f2331-c0f2-471b-bffe-b21097f6ff49",
+   "metadata": {},
+   "source": [
+    "## 4. Integrating the first law to arrive at the moist adiabat\n",
+    "\n",
+    "This example shows how to construct a moist adiabat allowing for equilibrium freezing.  To do so it makes use of two calls of the moist_adiabat function.  The first calculates the moist adiabat assuming condensation only produces ice, the other only liquid, with the latter being valid for temperatures above T0, the former for temperatures below T0, and an isothermal T0 layer residing in between.  The result is plotted in terms of the dry potential temperature to better highlight the enhanced stability."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "4a05ea68-9c61-449b-9945-d8f87fbb057a",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/m219063/opt/miniforge3/lib/python3.9/site-packages/scipy/optimize/_minpack_py.py:175: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
+      "  improvement from the last ten iterations.\n",
+      "  warnings.warn(msg, RuntimeWarning)\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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OpUEmoBIUcCdwKVCcW6/C+ncKHi+qH0j7iBSjlsL+NIgMhQlXQXio9+oeMWIExhjEV4uWB7iAucUTkWrAi8ALwEkRiXUOGwgDQp2/RwHHnC85q/UDxJG/ZXWsiHLgphVmjIkt6gdtPQWVeTvgyy3W8ye6WFNaPGWM4ZlnnmH27Nn5jmtyKlzAJCisTvEqWAkq2eWnE1ZfUTIwEtjkLO+u/6gF+fumNgHNnN8KFiwH7vuxVDlx5CQ8vth63uVvMLRl6eqbNGkSo0ePZvDgwTrOqZgCZpiBiERj3d4V9CoQDQwH9hpjdorIaqzk285lmEECsAi42Rgz3XmsL/ANcK0xJu/Pmoj8CNQwxjT1IM4U0GEGgc4YuGMOfL8LYiJh4a1wXnTp6kxMTOTKK6+kSZMmfPLJJ4SFBVoPi88E1zgoVyKyhLPHQfXAGvP0FTCZMwM19wKdjDE5znICfA+05MxAzWHAUGCAMWaOB/GkgCaoQPfp7/Cf763nr/eGAU28U29ycjLR0dHlfdxTQUE3DqpIxpjFwDVAA6yBmK84H6/OTU7Ocga4FpgOPA98h5WsBnmSnFRw2JMCo52bH/S7sHTJ6fPPPyclJSXv96pVq2pyKoGAb0H5G21BBbYcB9zwJaw5CDUrwYJbITbKs7omT57MXXfdRdu2bVmwYAFxcaXoYQ9u5asFpZSn3v7VSk4AL/X0PDkBREdHExoaSkxMDBUqVPBOgOWM9tIp5bQpEV5xfrk2tCV0rV+6+m655RZq1KhBhw4dNEF5SG/xvExv8QKT60TgRrEw9xbP5todOHCA2rVrez2+IKe3eEoVJd9E4Ks8S05Lly7l/PPP59VXX/V6fOWVJihV7q1wmQh8Xzto7eFE4FdeeYX09HTefPNNTp486b0AyzFNUKpcSyswEfj+9p7XNX36dO68804WLVpEpUqVvBZjeaZ9UF6mfVCB5dEF8MUWayLw3FtKN9dOeUz7oJQqaN4OKzkBPN655Mlp7969JCQksHv3bq/HpizagvIybUEFhiMn4aqPISkdOteDaQMhpASLCjgcDtq2bcu6deto1qwZGzduJDTUi+uwlC/aglIqlzHWPLukdGsi8Es9S5acwNqv7vXXX6dmzZq89dZbmpx8RFtQXqYtKP/nzYnAp06domLFit4JrPzSFpRSULqJwKdPn2bq1Km4/lHX5ORbmqBUuZHjgIcXwKksayLws1cU/7UOh4Nhw4Zx2223cc8996B3HmVDE5QqN1wnAo8v4URgh8NBZGQkAPXq1dNlesuI9kF5mfZB+SfXHYH/r2XJWk+5jDHMmTOHfv36aYLyruBdUdPfaILyPxnZ0H86bHVOBP72FqhYzLl2aWlpVK5c2afxKe0kV+XYy8ut5JQ7Ebi4yenLL7+kcePGusGBjbQF5WXagvIvK/bBTV9Z/6EfaA8Pdyje6zIyMrjwwgv566+/6NGjB4sWLdLbOt/RFpQqf0ozETgqKorFixfTt29fPv/8c01ONtEWlJdpC8p/eDIRWPucbKEtKFW+zP+zZBOBExMTuemmm+jSpQtZWVm+D1AVi8drkovIpcBlQFXOTnTGGDOmNIEp5anEk2emsnSuB8Nanfs1u3bt4osvvsDhcPDpp58ydOhQ3wapiqXEt3giUgGYAfTCapoZzjTRcp8bY0y5nD2pt3j2MgaGz4FFzh2BFwyBWsW8Yxs1ahT16tXj9ttv1z6nsuW9cVAi8gLWLrzPYe3K+wPWbrxHgMeBCsBQY8xWT6MNZJqg7PXZJhixyHr+2lVwrZvN640xvPPOO6xcuZIpU6aUbYDKHa8mqO3Ar8aYm0QkHkgErjTGLBaRMGA1MM8Y83hpIg5UmqDss/c49P4YTmbBNRfAxKvBXUNo7ty59O3bF4AZM2YwcODAMo5UFVBogvKkD6oe1lbiALnbiEcAGGOyReRT4B6s1pRSZcJh4NGFVnKqXtGaylLYXdrVV19N7969qVatGl27di3bQFWJeJKg0lxelwY4ANeNwI4DHu6LoZRnpqyFlfut5y9eCVVd9sncsGEDq1atYvjw4QCICLNmzcqb/Kv8lyfDDP4ELgQwxuQAm4DBAGL1LA4C/vJWgEqdy7ZjMH6Z9fyW5tCj4ZlzCxcupG3bttxzzz1s2LAh77gmp8DgSYJaBFwnIrnf0r0N9BaRP4HtwJWA9jyqMnE6Bx6cD5k58Lcq8GSX/Oc7d+5Mo0aNaNSoEZmZmfYEqTzmSSd5NFAH+NMYk+089jBwK1af1JfAi6acDlHXTvKy9dJyeGOV1cv6xWC4KPYkW7Zs4dJLL80rs2PHDurUqUOFChUKr0jZSZdbKSuaoMrObwfhui+sDvK720KfyusZPHgwKSkpbN68merVq9sdoioe70x1EZHqInKZiDQufUxKeS49y1q+12GgaTw8fDnEx8eTmJjI8ePHWb58ud0hKi8o1rd4IhICvAUMx5ntRGQ5MNAYk+i78JRy74VfYFcKhJlsJlwVRmQY1K1bl48++oj69evTokULu0NUXlCsWzwR+RfwKnAAWA5cALQEZhljBvkywECjt3i+99MeGPJVFscXPEvs3rlsX/cLERERdoelPFfqW7yhwBagmTHmemNMa6xv6vqJSGypw1OqmI5nwKOL4PT+9aQueJa9W9bw5ptv2h2W8pHiDtRsAow2xqS5HHsDuANrTNQqbwemlDvPLIVDJyC20aUMemAElcKyueeee+wOS/lIcRNUJazbO1cHXM4p5XOzN2Uw8w9rr6gnu8CQe5/XVQeCXEm+xSvYX5L7u35ClM9t/+so13e5kOOLxtKlbjZDWqDJqRwoyVy8PiLiOseuIlaSul5EWhcoa4wxE0obnFK5Bt//LFnJf5G26AUeeun/EKljd0iqDJQkQd3i/CnoLjfHDKAJSnnF3O2Q1PE5opMc3NKzNW2baHIqL4o7zKBbSSs2xiz1KKIAp8MMvCspHXpOg6Pp0K0+TB1Q+DIqKmCVbj2o8ppslP0en3eSo+mVqBwBYxM0OZU3uquL8lv/nTiDKbddwKnf5/BkF6itu0GVOx5NFhaRDsB9WCPK4zm7iWaMMeVyvp7e4nlH4okc6jVqQmbin9S+pDd/rZlLSIg2n4KU95b8FZGhwPtAFrAN2Ot5XEq5N+qnUOLvXkTa1w8z6+PXNDmVU56sB7UVa92nK40xBQdvlnvagiq9udvhnrnW83EJcFNze+NRPufVnYXrA//T5KR8Yc+RNJ5clA1Y39rdeLHNASlbeZKg9gG6oLPyiZ433MWmsR0JP7ZZv7VTHiWoScAQlzXJlfKKd+f9zvaln3J672p6hC7Tb+3UufugRKTgxmEhwAtYe+G9CezizP54eYwxP3opxoLxdAeeANo7Y9gNvGqMmexSpicwBmiFtTXWTODfxpiUAnVFA88D1wOxWDvUjDbGfF2K+FJA+6BK6sRpa0DmzvU/Er15GtsXTNaO8fLD8zXJRcTB2f8juVbo7pwxxni9hSUiw7DWoXoHmI31TWJTrPcx0VmmO7AQmIW140xtYBywE+hijHG41LcQaIO1lfsu4DZgCNDPGDPXwxhTQBNUST29BKauh8hQWHArNIi1OyJVhkqVoIZ5ckVjzFRPXldEHPWArcBIY8yLRZRbBYQDbXOTkbNFtQC4yRjzmfNYH+BbYJAxZqbzmAA/AfHGmGYexpkCmqBKYum2NIZ9VxkDPN4J7r70nC9RwSXwd3URkZFYLZ14Y0x6IWXqYHXiP2KMeaXAuX3AMmPMDc7f38G6tYsr0Kq6E5gMXGyM2exBnCmgCaq4Uk9mUrtJG0ytNnQYPoF5d1YjTOc3lDdeHWZgl65Yyw4PEpGtIpIjIvtEZKyI5C5InTti5nc3r9/ocj637GbX5OS0weX8WUQkpagfoIonb668uvO5jzi5fzOnfvuUOxvv1eSk8inxSHIb1Xb+vAE8hdWh3QN4HKiH1XcU7yyb5Ob1SVj9TbnisUbCuyuXe1750LZjsKbm7cTd6KBN9CFuvLLNuV+kypVASlAhQGXgZmPMdOexJSJSAXhURJ5xKVvYrVNhq4IWp6x18By3brm3eKpoOQ4YsQiyCeHi3nfy9RC7I1L+KJAa1Mecj/MLHP/O+djGpYy71k8c+VtWx4ooB+5bYcpL3ll5krWHrOcvJECFcHvjUf4pkBLUxkKO53awObBu+8B9/1EL8vdNbQKaOTclLVgO3PdjKS9YtWkv9/VqwPGFzzO4SRad6tkdkfJXgZSgZjgf+xQ43gfrdmy1MWYfsAZrpHveexORBKCOSx1gDd6MBfoVqG8osNWTb/DUuRkD//fgaHJOHOXkT6/zr1Yn7A5J+bHibn3+F9bAx1nAEmPMWSPHfc0YM09EvgPeFJFqnOkkfwCYZIzZ4yz6b6wxT5+KyGTODNRcCXzhUuVc4AdgiojEYw3UHAZ0BgaUwVsqlxbshFM9X6VyTiz/vPZy6teqandIyo8Vd03yN4H+WK2QFKwBjjOA+caYU74MsEAclYBRwM1Aday1qN4FXiwwlqm3s1zuVJdZwAhjTHKB+mKwproMxmpNbcaa6jKrFDGmgI6DcufkaUiYBgdP6PriKh/vDNQUkfbAQOBarN2GM7CmlcwE5hhjjhX+6vJBE1ThRv2QzXsbwogMhYW3Qv1YuyNSfsI7AzWNMauMMY87p4FchDUh9zys+XGHROQHEfmXiNQvVbgq6Mz4YT1jrmvMqXVfcl87o8lJFYtXpro4p5jktqy6AqHAeuAJY8y8Ul8ggGgL6mwOAzVbJHB002Iq1mrK4T83EK3jCtQZvp3qYozZb4yZaIy5EqgB3I61DIou1qqY/jtEDJpC1MXXMP61/2lyUsUWMJOFA4W2oPI7egqu+BBSM2FwM3i5l90RKT8UFJOFVQAa86MhNROqRMITne2ORgUaTVDKZ9747Acm3d2R0/vW8XhniK9od0Qq0OgtnpfpLZ7lZEY21Rs2J/3QVqo168rhTUvRFXxVIfQWT5WtDzaGUfm6/xFRpzVTJk3U5KQ8UuwWlIjcgbUCZQzWtJHxujfe2bQFBQfSoMeHkJ4Nwy8xPNVVs5MqUum2Pncug/u2y6HLgZtEpJMxZmcpg1NB5rmfrORUvSI8eJkmJ+W54t7i3Qv8BXTAWr3yTqAi8LKP4lIB6vXpi5k66nZy0g7zRGeorFu8qlIo7mThVKxJtC+5HHsIa5WAqsaYk74LMbCU51u8UxlZ1Di/NSf3b6Zm694c/O07nQysiqPUneTRQMH+pnlYt4hNPAxKBZmPNoYQ0fFfhETX4M2XX9DkpEqtNN/iHXE+xngjEBXYjpyE19aEUrnTXTz25R6u69Ha7pBUECjJpgl9RSQZWGOMSXQ5rkMVFGN/sbYvrxoF/+kWZXc4KkiUJLncDHyDtazKbmAqVh/KRSKiyyKWY1NmL+O9N8ZisjP5dyeI1fykvKS4neSVsXZNaQO0dT5eiJXgcis4gLXp5QZgvcvWUOVKeeskP52VQ7ULLiVtzzpqXX4Df/3yGaHaplYlU7pxUMaYNGCp88eq0Vp+tzVnElZboBdwNdb/eOUyQZU309aehoY9YN8mxj71sCYn5VVenYsnIlHAJcAlxpi3vFZxAClPLajjGdBtKiRnwNU1DzLpplp2h6QCU+laUMVljMkAljt/VJB7bZWVnCqFw+h+mpyU92mDXHnk+zXbeWvabIwx3NcOalSyOyIVjHS5FS8rL7d4f2vfn79Wz6FG59vZ88N7RHm1La7KGV1uRXnPoq3pJKZlAfD3G/poclI+oy0oLwv2FlS2A/p8AluPQaPUn/n+v50I0cWeVOmUTSe5Cn7Tf7eSkwCv/6MzIdoGVz6kHy9VbHsPp/DsjE0ADL4IWtS0OSAV9DRBqWK75YFn2Tq6JSe+GcFjHe2ORpUHmqBUsWxPzGL1j/PBOOh4QSw1dViBKgPaSe5lwdpJ/o9vYN7W04Svf481bw6jauUKdoekgod2kivPrdwP8/8ECYvg1SfvpmpluyNS5YXe4qkiORyGUfOPA3DJeXDNBTYHpMoVTVCqSP+d+CXz729E6pIJPN7J6DK+qkxpglKFysw2vPHy8zhOJVHl0I9cVlezkypbmqBUoT75XYi9cz4xXe7j7Qkv2B2OKof0WzwvC5Zv8VIzrbWektLh1hbwXA+7I1JBTCcLq5KZ9KuVnCqGwwOX2R2NKq80Qamz/PrHPp6+uT3pm+fyj0uMrvWkbKO3eF4WDLd4LXr/nd/nv09YTE0O7NlJ9diKdoekgpsO1FTF88dRONr8PiJ37eWWG6/X5KRspS0oLwv0FtSwWbBkDzSKNcwfYogI014A5XPaglLntmKflZwAnugiRITpuCdlL/3zqABrSsttDz5N1uGttK0FVza0OyKlNEEppxfe+5atX43h4LiLubnWNp3SovyC3uIpHAZmbA0hNL4hNepdwPVdLrQ7JKUATVAKmLMNjtbtQ+3H/2BqryS7w1Eqj97ilXNZOfCKcx/ovk0juKLFefYGpJQLTVDl3ItfrmHn4VRCBB7uYHc0SuWnCaocS05LZ9TdAzgwphFtTszjgji7I1Iqv4BKUCJyiYjMEpEDInJSRDaLyH9EJLJAuZ4iskJE0kXkiIi8LSKxbuqLFpHXReSgs+waEelfZm/IZi98/ivZp1JwZKTyWP9mdoej1FkCppNcRJoCy4CtwIPAUaAH8BxwETDUWa47MBeYBTwJ1AbGAc1FpIsxxuFS7UygDTAC2AXcBswUkX7GmLk+fku2SsuEBdmdqf3UTjrm/MzlzevbHZJSZwmYqS4iMhJ4BjjfGPOny/FpwE1ARWNMloisAsKBtrnJSER6AguAm4wxnzmP9QG+BQYZY2Y6jwnwExBvjPGoSREoU11eXQETVkKFMPjpNqiuKxYo+wTFelBZzsfjBY4fd57LEZE6QDtgmmtLyRizENgPXOfyuoHO1852KWeAqUBTEbnI6+/ATxxKyWTyb1Zu/PslmpyU/wqkBDUNSAL+JyINRSRGRAYAw4CXnQmpubPs725ev9HlPM7nmwvc8gFscDkflG6+fyQ7nm+DbP+Ou9rYHY1ShQuYPihjzF4RuRyrb2mny6nnjTFPOZ/HOx/djTZMwupvwqXstkLKudaVT+4tXBGqcHYrz2/sPpTKj19MxJF5gmanV1Ml6mq7Q1KqUAGToESkPjAHOIR1e5YCdAMeFxGHS5KCwvt2Ch4vqg8oMDrnSujTHTFUv/d70pe+xORnH7A7HKWKFDAJChgLVAYuMcakO48tsfq1eVpEpgDHnMfdtX7iyN+yOlZEOXDfCjtn53cxWli2OXYKpq6HyPrteeJ/n1Ovht0RKVW0QOqDugSrzyi9wPE1WO+jKbDJecxd/1EL8vdNbQKaiUjB/wYtnI/u+rEC2tu/QXo2xEbB7a3sjkapcwukBHUAayxTwTVocydo7DfG7MNKWENcE4+IJAB1gBkur5sJxAL9CtQ3FNhqjNnsxdhtt3nXYcY9Moysw39w5yVQOfLcr1HKboE0DuparKTyM/AqVkd0d6xBlkuNMT2d5XpgjXn6CpjMmYGae4FOxpgcZzkBvgdacmag5jCsBDXAGDPHwzhTwP/GQXW+6VF++exlQitX5/D+fcRXjiirSyt1LoE/DsoYMwvoCWQCb2GNXxoIjAGudSm3GLgGaIA1EPMV5+PVucnJWc44XzcdeB74DitZDfI0OfmrIyfhz6g2hMU3os//PaTJSQWMgGlBBQp/bEGN/hGmrIXY8Cy+vzWHajFRZXFZpYpLN00orw6fhI+cQ0/vbh9OtZhwewNSqgQC5hZPeeaxSQtJP5lGXAUY2tLuaJQqGU1QQez3nYf46PH+HBjdgJ7hK6ikXU8qwGiCCmJjP1sFCBISwmMDW5yzvFL+RvugglRyOvxapT+1n9nDdXGbqB6rSxaowKMtqCD13jo4lQVV46oz5u/d7Q5HKY9oggpCx05k8f5aawTDsNYQo6PGVYDSBBWEbv/3S2x7oS05f8zh763tjkYpz2mCCjLJJzL5btoEsvatpWHKj8RVsDsipTynCSrIfLUtkvg75lCp5UDefPZhu8NRqlR0qouX2TnVJSMbun5gjR4f2hLGXOHN2pXymcCfLKzO7cvNVnIKC4G729odjVKlpwkqSJzKyGLEow+RdWgLg5pCnRi7I1Kq9HSgZpD494RPObjwVfh+Itfftg+oaXdIRTLGcPToUTIyMnA4Cm6sowJdSEgIUVFRVKtWDeey3B7RBBUEHAaWHKxMWLXGNLy4Pe2b+H9y2r9/P2lpaURGRhIaGmp3SMrLsrKyOHHiBJmZmdSpU8fjJKUJKggs+BNSGw+k1uP9+LBfqt3hnNPRo0dJS0ujZs2axMXFnfsFKiAlJSVx+PBhjh49SvXq1T2qQ/ugApwxMOlX63lC4zAuv8D//4fPyMggMjJSk1OQi4uLIzIykoyMDI/r0AQV4L5Z8xe/7jkBwN2X2hxMMTkcDr2tKydCQ0NL1ceoCSrA3XvvvRwY9TfitrxH+9p2R6OUd2kfVABbtuUI+9d/j8lK55qWVSnFlyVK+SVNUAHsq79qUPvp3UT9Po2n7uxvdzhKeZ3e4gWoA2kwayuEVq7BmCcfISJc+3T8wciRI/N9pS4ijBw5skyvWZSyiMebtAUVoKashWwHVK8IA5vaHY0qzPLly6lbt65PrzF8+HB69+7t02vYRVtQAWjPwWTGDr+CU+u+4LYWOUTpnxm/dfnll/s8QdWtW5fLL7/cp9ewiyaoAHT/mP9xavsSkqbfQb+GaXaH4xXZDvgr1X9+sr00+8bdLdWcOXNo1aoVkZGRNGjQgLFjx/LMM8/ku03bvXs3IsIHH3xwzjrd3eIdP36c4cOHEx8fT3R0NL169WLr1q3eeVNlSP/2BpiMbNheJYEKzVfStkUT6teMtTskrzh4Ajq/b3cUZ/x8O9TzwYTrBQsWcO2119K5c2emT59OdnY248aN48iRI167hsPhoH///qxcuZKRI0fStm1bfv75Z66++mqvXaOsaIIKMDO2wKnzLqP2P2YzfahOsg00Tz31FLVr12bBggVERlqLxffq1YuGDRt67Rrz58/nxx9/5M033+Tee+8FoGfPnoSFhfH000977TplQRNUAHEYeOc36/mAJlCnSvDcodeKtlot/qJWtPfrPHnyJKtXr+aBBx7IS04AVapUoV+/fnz44Ydeuc6SJUsAuOWWW/Idv/XWWzVBKd95d+56tm6rQHiNC/lHG7uj8a6wEN/cUvmT5ORkjDGcd955Z52rVauW165z7NgxoqKiiI2N9dk1ykrw/AkuB576z8McfL4JVZaNpEk1u6NRJVW1alVEhEOHDp117uDBg/l+j4qKAiAzMzPf8WPHjp3zOvHx8WRkZJCSklLkNQKBJqgAsWJHCkkHdwNwa5/g/Eo52FWqVIn27dvz1Vdf5Us8qampzJkzJ1/ZmjVrEhUVxYYNG/Idnz179jmvc8UV1mL0n3zySb7jH330kaeh20Zv8QLEFztjqfXfbVTdN49H/+8qu8NRHhozZgy9e/emV69ePPTQQ2RnZzN27Fiio6NJTk7OKyciDBkyhPfee4/GjRvTqlUrVq1adVbScadXr1507dqVRx55hNTU1Lxv8aZNm+bLt+YTmqACwOGTMHsrSEgo/76tLyHa7g1YPXv2ZNasWTz55JPceOONnHfeedx7772kp6czatSofGVfeeUVRIQXX3yREydO0KNHD7755hsaNGhQ5DVCQkL4+uuvefjhhxk3bhynT5+mU6dOfPfddzRtGljTDnTbKS/zxbZT45cZJq4WqkbBijsI+JHje/bsAaB+/fo2R+I/Ro4cyahRowi2/x+L+W+t204FquS0dJ667mJS5j7NoAZJAZ+clCoJTVB+7rGXppF5aAupi8cx6ILTdoejVJnSBOXHjIE/qvUjpteTtO1/H80bnT1+RgWHkSNHBt3tnTfoDYMfW7oH/nLUIrbPGD685dzllQo22oLyY++utR471oWLPNu1R6mApgnKT81buY3538zEOHIYHmTTWpQqLk1QfurjWQs5+t4gkt/qxhUN7I5GKXtogvJTWVlZAMjpE4Tobi2qnNJOcj/V9bq7+TluKM2qa3ZS5ZcmKD8VGhFFaKUoIn2wLpFSgUJv8fxU7pCYUG1ABb2Ca4yvWLGCkSNHnrVcSm7ZBx980KPrLFmyBBHJW9AuEGiC8lPHDu0jc/cK0vZvtjsU5WPLly9n+PDheb+vWLGCUaNGuU1QpdGmTRuWL19OmzaB87Ww3uL5qRXfTuXwpCfJurAjPPKL3eEoHyqrLaNiYmICbnsqbUH5KYfD2hChuDvGKnutX78eEcm38NzixYsREbp165avbJs2bbjxxhvzfne9xRs5ciQPPfQQAA0bNkREEBF2796dr44PPviApk2bUrFiRVq1asU333xzzhgLu8WbO3cuV1xxBVWqVKFSpUo0b96cN95446wy3bp1o3LlylSqVImEhARWr159zmuWlu0JSkTqishrIvKziJwQESMi3Qsp21NEVohIuogcEZG3RSTWTbloEXldRA46y64Rkf6lqbOsJQx9nHrj0+n29CK7QylTu3fvZvfu3WRkZOQdczgcecddV6LMycnJO3769JmJ1NnZ2XnHc4drgDV0I/d4dnZ23vHTp0/nHc/9w1BSLVu2pHr16ixadObf6/vvv6dChQqsWLGCU6dOAdaSvevWrSMhIcFtPcOHD8/rY5oxYwbLly9n+fLl+dYTnz17NpMmTWLMmDF89dVXxMXFMXDgQHbu3FniuCdPnkzfvn0JDw9n8uTJzJ49m7vuuitvmRSA9957j2uuuYY6derwySef8PHHH5OVlUW3bt3YuHFjia9ZIsYYW3+A7sARYB4wG2uNpO6FlMsCvgCuBIYCB4FfgJACZRcCx4A7gB7Ah0AO0MfTOkvwflKAlGKWL9TLy4z526vG3PBlUaUC0+7du83u3bvdnnP++5sffvgh79jJkyfzjq9cuTLv+NGjR/OOb9iwIe/43r17847v2LEj7/jWrVvzju/fvz/v+Nq1a/OOJycne/y+brzxRnPRRRfl/X7ZZZeZBx980ISHh5t58+YZY4z57LPPzooLMM8880ze7xMmTDCA2bVr11nXAEzt2rXNiRMn8o4dOnTIhISEmOeff77I+H744Yd8/21TU1NN5cqVTY8ePQp9zYkTJ0xsbKy5/vrr8x0/efKkqVOnjhk8eHCR1yzq39pFof+P2N6CAn40xtQwxvQGitq68UXgd+BGY8wiY8yHWAmlI3B9biER6YOVbIYbY6YYYxYDw4DlwMue1GmH3L/j/vAPpIonISGBzZs3c/DgQY4fP86aNWsYMGAAl19+eV7LatGiRdSvX5/GjRt7fJ0ePXpQqVKlvN9r1qxJjRo18rV6imPZsmWkpaVx9913F1pm+fLlpKSkcOutt5KdnZ33ExERQffu3Vm6dKnH76M4bO8kN8acs00tInWAdsAjruWNMQtFZD9wHfCZ8/BA4DhWayy3nBGRqcBkEbnIGLO5hHWWucS//iRj+16O58QDLe0Ko8zt2rULIN/WTFFRUXnHXW91YmNj847Xrl0773itWrXyjtepUyfveMOGDfOO16hRI+/4RRddlHc8Jsbzva9yb9sWLVpETEwMkZGRdOzYkYSEhLzNDhYtWlTo7V1xxcfHn3UsMjIy321xcRw9ehSAunXrFlrm8OHDAAwYMMDteV/3kdqeoIqpufPxdzfnNrqczy272U3i2+B6voR1lrlVc97lyEdjWde6Fzw8385QypS79bZDQkLcHg8NDXV7PCwszO3x8PBwt8cjIiLOuc53cTRq1IgGDRqwaNEiqlSpQufOnYmIiCAhIYFRo0axevVqdu3axbPPPlvqa3lD9erWEhn79u0rtEy1atb+Zm+99Rbt2rUrk7hcBUqCyv2TkeTmXBLQpkDZbYWUc62rJHXmyV1zvAhVsFpwpWIM4PwGRwWOhIQE5s2bR5UqVbjtttsAuOyyy6hUqRL//e9/AesWrSi5uw6np6f7NNaOHTsSExPDpEmTuP569z0anTp1IiYmhj/++IN77rnHp/G4EygJKldhSw4WPF7U0oTFLWvr8oY973qBXe1eoHt9XWUxkCQkJDBlyhT279/PlVdeCVgtt65duzJ37lwuvvhitzsLu2re3Gq8T5w4kVtvvZXw8HBatmxJRESEV2ONjo5m/Pjx3HXXXfTq1Yvhw4dTrVo1tm7dys6dOxk/fjzR0dG8+uqrDB8+nKSkJAYOHEh8fDyHDx9mzZo1REZGMmbMGK/G5SpQ+mBzt1M9++Yb4sjfCjpWRDlcypakzjzGmNiifvBC6wnAkTvVRZcyCCg9evRARIiPj6d169Z5x3P7nYrT/9SlSxf+85//MGPGDDp37ky7du04cOCAT+L9xz/+wddff016ejp///vf6devH2+99Va+XVhuv/12FixYQGJiInfccQdXXXUVjz32GH/++Sddu3b1SVy5/GrbKRG5FpgJXGGMWeJyvC7wF1aH9isFXrMPWGaMucH5+7tYHdzxrv1QIjIceAe42NlJXuw6S/geUqD0206NXgpT1kHPRvBuv5JG4d9026nyo1xsO2WM2QesAYaISF7MIpIA1AFmuBSfCcQCBf+3HgpsNcZs9qDOMndo5++kb/qWpD9/szMMpWzlF31QIjLY+TT3a4JuIlINOGmM+c557N/AAuBTEZkM1AbGASuxBlrmmgv8AEwRkXhgF9Y4qM5Awe9Ki1tnmVsz520SZ05kbYdB8OBXdoailG38IkFxdjIY6XzcAzQAMMYsFpFrgFHAt0AaMAsYYYzJyX2hc8zTtcDzzp9YrGEFg4wxZyZKlaBOO0hoOBJRkbCIKDvDUMpWftUHFQy81Qf138Xw0Ua45gJ4s4+XgvMT2gdVfpS2D8pfWlCqgCc6w8OXQ1io3ZEoZR9NUH6qUoT1E4xCQkLyrTKggldOTg7h4eEevz4gvsVTwSUqKorMzEySktwONVNBIikpiczMTKKiPO9H1RaUKnPVqlUjMzOTw4cPk5KSQmio3scGm5ycHDIzM6lcuXLefD5PaCe5l3mrkzzYGWM4evQoGRkZHi8Sp/xXSEgIUVFRVKtWrTjzSQstoAnKyzRBKVVigT2SXClVPmmCUkr5LU1QSim/pQlKKeW3NEEppfyWJiillN/SgZreV5IVNXW5TKWKoOOglFJ+S2/xlFJ+SxOUUspvaYJSSvktTVBKKb+lCUop5bc0QSml/JYmKKWU39KBmjYRkT1AFbvjUMoPHDfGuN32RVtQgaUKmtTKu3L1GdCR5AGkhKt1qiBU3j4D2oJSSvktTVBKKb+lCUop5bc0QSml/JYmKKWU39IEpZTyW5qglFJ+S8dBKaX8lraglFJ+SxOUUspvaYJSSvktTVA2EJGOIjJfRPaLSIaIJIrIYhG52k3ZniKyQkTSReSIiLwtIrFuykWLyOsictBZdo2I9C+TN6RKrLifARFZIiLGzc90N3UG3WdAE5Q9qgJbgUeA3sA/gExgrojclFtIRLoDc4G/gH7Ao0B/4FsRKfhvNxMYAjwJ9AU2AzNFpI8v34jyWLE+A07bgQ4Ffp50U2fQfQb0Wzw/ISJhwC5guzGmh/PYKiAcaGuMcTiP9QQWADcZYz5zHusDfAsMMsbMdB4T4Ccg3hjTrKzfjyq5Qj4DS4BYY0zrc7w2KD8D2oLyE8aYbKxdibMARKQO0A6YlpucnOUWAvuB61xePtD52tku5QwwFWgqIhf5/A2oUiv4GSihoPwMaIKykYiEiEiYiNQWkVHAhcAE5+nmzsff3bx0o8v53LKbXROZ04YCdSk/c47PQK4mIpIsItkisl1EnhSR8AJlgvIzoEv+2utzzrSEUoEbjDHznL/HOx+T3LwuCWjj8ns8sK2Qcq51Kf9T1GcArFu06cAfQDRwLTAaaIvVasoVlJ8BTVD2GgGMA84DbgE+F5FhxphPXcoU1klY8HhRnYna0ei/ivwMGGOeKlD+GxE5DDwhIp2NMT+7nAu6z4De4tnIGLPTGLPaGDPHGHMzMB940/kN3TFnMXd/+eLI37I6VkQ5cN8KU37gHJ+Bwkx1PnZwORaUnwFNUP5lFdbXz9WBTc5j7voOWpC/b2oT0MzNh7qF89FdP5byT66fgcLk/ju79jcF5WdAE5SfcH4l3B1IAY4ZY/YBa4Ahrh86EUkA6gAzXF4+E4jFGivlaiiw1Riz2WeBK68p+BkoouhQ5+MKl2NB+RnQPigbiMjHwB7gV+AoUAsYBvQA7nd+3Qzwb6wxT5+KyGSgNlZ/xUrgC5cq5wI/AFNEJB5rLM0woDMwwOdvSJVYcT4DItIF+A/wlbNsJax/z9uBL4wxv7hUGZyfAWOM/pTxD3AfsBzrr2S283E+0M9N2d5YCSkDSATeAaq6KRcDTAQOOcv+Blxr93vVH88/A8D5WIMv9zn/TU8Ba4EHgdDy8BnQkeRKKb+lfVBKKb+lCUop5bc0QSml/JYmKKWU39IEpZTyW5qglFJ+SxOUUspvaYJSSvktTVAqoInIVc6NBU44Nx6YKCJRdselvEMTlApYIvIIMA84CDwEzAH+CbxWgjredO6sIkWU6e7cSeVRN+e6ichx504qLUv+LlRRNEGpgCQiVwLjgceMMTcbY94xxvwdaz7bbSISU4w6BGsi7WzjwZwvEbkGK0EmAV2MMRvO8RJVQpqgVMBxLj/zGtbE2ZcLnF4CRFC8NbjbYS1dM8uDGG7BWuJkJ9DJGLOjpHWoc9MEpQLRVcBFwOtuWj6nnY9VilFP7k4oP5Tk4iJyDzANa7WArsaYAyV5vSo+XQ9KBaIbgRzgJxGpVuBcTedjWjHqGQh8a4wp9jZPIvI48DywGBhgjDlR3NeqktMEpQLRFUAo8GcRZXYWVYGINAOa4H6H3sLcAzTCuiW8yRiTWYLXKg9oglIBxdli+htW/89bbop8DmQW47brWqytxuedo5yrWs7HnZqcyoYmKBVoGjkfVxtjFrmeEJGGWBsOfFKMegYCC0t4izYW6AY8LCIYYx4pwWuVB7STXAWaaOejuz6mwc7Hz4qqQETqApdS8m/vTgHXAN9jJamCOwArL9MEpQJNqvMx3zgnEYnA6iPairWOd1GuxdrI8uuSXtwYk461c8oi4EERebWkdaji0wSlAs1mrJbMVQWOPwc0AP5ljMk5Rx0DgZ+NMYmeBOBMUv2BhcADIvK6J/Woc9MEpQKKMeYU8C7QVUQ+EpE7RWQG8CgwwhizoKjXi0hVoCseDM4sEEdukloA3C8iE0tTn3JPO8lVIHoM6xZtCFZr6FfgamNMcb6R64f1uZ9V2iCMMRkiMsBZ1z+dU2fu82TajHJPt51S5YqIzAQaGmNa2x2LOjdtQanyZjnW5qcqAGgLSinlt7STXCnltzRBKaX8liYopZTf0gSllPJbmqCUUn5LE5RSym9pglJK+a3/B//U+KuqfmruAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<Figure size 288x360 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "qt   = 16.774409538883497e-3\n",
+    "Tice,Py= mt.moist_adiabat(Tsfc,Psfc,150e2,-10.,qt,cc=constants.ci,l=mt.sublimation_enthalpy ,es = mt.es_mxd)    \n",
+    "Tliq,Px= mt.moist_adiabat(Tsfc,Psfc,150e2,-10.,qt,cc=constants.cl,l=mt.vaporization_enthalpy,es = mt.es_mxd)\n",
+    "\n",
+    "Tx  = np.ones(len(Px))*constants.T0\n",
+    "Tx[Tliq>constants.T0] = Tliq[Tliq>constants.T0]\n",
+    "Tx[Tice<constants.T0] = Tice[Tice<constants.T0]\n",
+    "Tx   = np.maximum(Tx,190.)\n",
+    "Tliq = np.maximum(Tliq,190.)\n",
+    "\n",
+    "Tl2T    = np.vectorize(mt.T_from_Tl)\n",
+    "Tl = mt.theta_l(Tsfc,Psfc,qt)\n",
+    "TK = np.maximum(Tl2T(Tl,Px,qt),Tmin)\n",
+    "\n",
+    "sns.set_context('talk')\n",
+    "fig, ax = plt.subplots(figsize = (4,5), constrained_layout = True, sharey=True)\n",
+    "\n",
+    "ax.plot(mt.theta(Tliq,Px) ,Px/100.,label=f\"liquid\",c='dodgerblue')\n",
+    "ax.plot(mt.theta(Tx,Px)   ,Px/100.,label=f\"with ice\",c='k',ls='dotted')\n",
+    "\n",
+    "plt.gca().invert_yaxis()\n",
+    "\n",
+    "ax.set_xlabel(\"$\\\\theta$ / K\")\n",
+    "ax.set_ylabel(\"$P$ / hPa\")\n",
+    "ax.legend()\n",
+    "\n",
+    "sns.despine(offset=10)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "dbbb919e-7911-403e-8d4f-b59cd3464650",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "q=[0.,0.,0]\n",
+    "print (np.sum(q))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b4eb7eab-22a7-4988-b99c-835da8557f83",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
diff --git a/moist_thermodynamics/functions.py b/moist_thermodynamics/functions.py
index e0c0f42..3ba9178 100644
--- a/moist_thermodynamics/functions.py
+++ b/moist_thermodynamics/functions.py
@@ -322,6 +322,35 @@ def saturation_partition(P,ps,qt):
     qs = partial_pressure_to_mixing_ratio(ps,P) * (1. - qt)
     return np.minimum(qt,qs)
     
+def theta(TK,PPa,qv=0., ql=0., qi=0.):
+    """Returns the potential temperature for an unsaturated moist fluid
+    
+    This expressed the potential temperature in away that makes it possible to account
+    for the influence of the specific water mass (in different phases) to influence the
+    adiabatic factor R/cp.  The default is the usualy dry potential temperature.
+    
+    Args:
+        TK: temperature in kelvin
+        PPa: pressure in pascal
+        qv: specific vapor mass
+        ql: specific liquid mass
+        qi: specific ice mass
+
+        es: form of the saturation vapor pressure to use
+    
+    """
+    Rd   = constants.dry_air_gas_constant
+    Rv   = constants.water_vapor_gas_constant
+    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
+    P0   = constants.P0
+    
+    qd    = 1.0-qv-ql-qi
+    kappa = (qd*Rd  + qv*Rv)/(qd*cpd + qv*cpv + ql*cl + qi*ci)
+    return  TK*(P0/PPa)**kappa
+
 def theta_e_bolton(TK,PPa,qt,es=es_liq):
     """Returns the pseudo equivalent potential temperature.
     
@@ -727,3 +756,71 @@ def zlcl(Plcl,T,P,qt,z):
     cp = cpd + qt*(cpv-cpd)
     R  = Rd  + qt*(Rv-Rd)
     return T*(1. - (Plcl/P)**(R/cp)) * cp / g + z
+
+from scipy.integrate import ode
+
+def moist_adiabat(Tbeg,Pbeg,Pend,dP,qt,cc=constants.cl,l=vaporization_enthalpy,es = es_liq):
+    """Returns the temperature and pressure by integrating along a moist adiabat
+    
+    Deriving the moist adiabats by assuming a constant moist potential temperature
+    provides a Rankine-Kirchoff approximation to the moist adiabat.  If thermodynamic
+    constants are allowed to vary with temperature then the intergation must be
+    performed numerically, as outlined here for the case of constant thermodynamic 
+    constants and no accounting for the emergence of a solid condensage phase (ice).
+    
+    The introduction of this function allows one to estimate, for instance, the effect of
+    isentropic freezing on the moist adiabat as follows:
+    
+    Tliq,Px= moist_adiabat(Tsfc,Psfc,Ptop,dP,qt,cc=constants.cl,l=mt.vaporization_enthalpy,es = mt.es_mxd)
+    Tice,Py= moist_adiabat(Tsfc,Psfc,Ptop,dP,qt,cc=constants.ci,l=mt.sublimation_enthalpy ,es = mt.es_mxd)    
+    
+    T  = np.ones(len(Tx))*constants.T0
+    T[Tliq>constants.T0] = Tliq[Tliq>constants.T0]
+    T[Tice<constants.T0] = Tice[Tice<constants.T0]
+    
+    which introduces an isothermal layer in the region where the fusion enthalpy is sufficient to do
+    the expansional work
+   
+    Args:
+        Tbeg: temperature at P0 in kelvin
+        Pbeg: starting pressure in pascal
+        Pend: pressure to which to integrate to in pascal
+        dP:   integration step
+        qt:   specific mass of total water
+        es:   saturation vapor expression
+        
+    """
+    def f(P,T,qt,cc,l):
+        Rd  = constants.Rd
+        Rv  = constants.Rv
+        cpd = constants.cpd
+        cpv = constants.cpv
+        
+        qv  = saturation_partition(P,es(T),qt)
+        qc  = qt-qv
+        qd  = 1.-qt
+        
+        R   = qd * Rd + qv * Rv
+        cp  = qd * cpd + qv * cpv + qc * cc
+        vol = R * T/P
+    
+        dX_dT  = cp 
+        dX_dP  = vol
+        if (qc > 0.):
+            beta_P = R/(qd*Rd)    
+            beta_T = beta_P * l(T)/(Rv * T) 
+            
+            dX_dT += l(T) * qv * beta_T/T 
+            dX_dP *= ( 1.0 + l(T) * qv * beta_P/(R*T))
+        return dX_dP/dX_dT;
+    
+    Tx = []
+    Px = []
+    r = ode(f).set_integrator('lsoda',atol=0.0001)
+    r.set_initial_value(Tbeg, Pbeg).set_f_params(qt,cc,l)
+    while r.successful() and r.t > Pend:
+        r.integrate(r.t+dP)
+        Tx.append(r.y[0])
+        Px.append(r.t)
+
+    return np.asarray(Tx),np.asarray(Px)
\ No newline at end of file
-- 
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