collect_profiles.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a299760a",
   "metadata": {},
   "source": [
    "# Turning simulation output into time-averaged profiles\n",
    "AFiD outputs regular plane-averaged profiles $f(x,t)$ into the file `outputdir/means.h5` inside each simulation directory. This notebook loops over the simulations to combine the data into two databases of time-averaged profiles $\\overline{f}(x)$, containing data for all the simulations. These files are the CSV formatted `base_profiles.csv` and `ref_profiles.csv` which store data for variables on the coarse and refined grid respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3fb333f8-14e8-4f40-9d75-b6fd93f0f637",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Begin by loading the required pacakages\n",
    "import h5py\n",
    "import afidtools as afid\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "edf40f8c-cba4-46f4-90be-bbd0936c45f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create the list of simulation directories\n",
    "flist = [\n",
    "    \"Sc10/Pr1\", \"Sc10/Pr2\", \"Sc10/Pr5\", \"Sc10/Pr20\", \"Sc10/Pr50\", \"Sc10/Pr100\",\n",
    "    \"Sc100/Pr1\", \"Sc100/Pr2\", \"Sc100/Pr5\", \"Sc100/Pr10\", \"passive/Sc10\", \"passive/Sc100\"\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4c80d2e4-0cd5-401b-9503-ed7e639b50a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Collect wall-normal coordinate grid from each simulation,\n",
    "# for both coarse and refined grids, and store in a list\n",
    "xlist, xrlist = [], []\n",
    "for f in flist:\n",
    "    xlist.append(afid.Grid(f).xm)\n",
    "    xrlist.append(afid.Grid(f).xmr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "79986dc0-91a7-4512-bbb0-c6e2f2c41194",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Collect coordinates in time of the time series for each simulation\n",
    "tlist = []\n",
    "for f in flist:\n",
    "    tlist.append(np.array(afid.mean_time(f)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c10a7c29-760b-43f5-816c-eb89a61f51ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Specify when to start averaging over each simulation\n",
    "# N.B. These are chosen to avoid initial transient effects\n",
    "t0list = [\n",
    "    100, 400, 400, 900, 360, 450,\n",
    "    650, 400, 420, 400, 100, 860\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d33945b8-76fc-4600-9d77-c49472a2f8c0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Sbar', 'Srms', 'Tbar', 'Trms', 'chiS', 'chiT', 'epsilon', 'vxS', 'vxT', 'vxrms', 'vxvy', 'vxvz', 'vyS', 'vyT', 'vybar', 'vyrms', 'vzS', 'vzT', 'vzbar', 'vzrms']\n"
     ]
    }
   ],
   "source": [
    "# Construct a list of all the variables output by the simulations\n",
    "# These are explicitly defined in the documentation at\n",
    "# https://chowland.github.io/AFiD-MuRPhFi/mean_outs/\n",
    "with h5py.File(flist[0]+\"/outputdir/means.h5\",\"r\") as f:\n",
    "    varlist = list(f.keys())\n",
    "    print(varlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "61f3a2bd-8b0b-4ce5-8101-f47f41415bb0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialise lists to fill with DataFrames from each simulation\n",
    "dlst, drlst = [], []\n",
    "\n",
    "# Loop over the simulation directories\n",
    "for i, fld in enumerate(flist):\n",
    "    # Load the grid coordinates and time coordinates\n",
    "    x = xlist[i]\n",
    "    xr = xrlist[i]\n",
    "    t = tlist[i]\n",
    "    t0 = t0list[i]\n",
    "    \n",
    "    # Read physical input parameters from the simulation input file\n",
    "    inputs = afid.InputParams(fld)\n",
    "    RaT, RaS = inputs.active_T*inputs.RayT, inputs.RayS\n",
    "    Pr, Sc = inputs.PraT, inputs.PraS\n",
    "    \n",
    "    # Start building DataFrames with physical parameters and coordinates\n",
    "    df = pd.DataFrame(\n",
    "        {\n",
    "            \"RaT\": RaT, \"Pr\": Pr,\n",
    "            \"RaS\": RaS, \"Sc\": Sc,\n",
    "            \"x\": x[:x.size//2]\n",
    "        }\n",
    "    )\n",
    "    dfr = pd.DataFrame(\n",
    "        {\n",
    "            \"RaT\": RaT, \"Pr\": Pr,\n",
    "            \"RaS\": RaS, \"Sc\": Sc,\n",
    "            \"x\": xr[:xr.size//2]\n",
    "        }\n",
    "    )\n",
    "    \n",
    "    # Loop over variables to record\n",
    "    for var in varlist:\n",
    "        # Read array for times we want to average over\n",
    "        tmp = afid.read_mean(fld, var)[:,t > t0]\n",
    "        \n",
    "        # Simulation stores rms values including the mean.\n",
    "        # We want squared perturbation quantities, so we\n",
    "        # square the rms and subtract the square of the mean\n",
    "        if var in [\"vyrms\", \"vzrms\", \"Trms\", \"Srms\"]:\n",
    "            tmp = tmp**2 - (afid.read_mean(fld, var[:-3]+\"bar\")[:,t > t0])**2\n",
    "        # By definition vxbar==0, so no need to subtract a mean\n",
    "        elif var==\"vxrms\":\n",
    "            tmp = tmp**2\n",
    "        # Change the name of the rms variables in the DataFrame\n",
    "        # to reflect these are squared perturbations now\n",
    "        if \"rms\" in var:\n",
    "            vname = var[:-3]+\"p2\"\n",
    "        else:\n",
    "            vname = var\n",
    "        \n",
    "        # Through the problem setup, all mean profiles are anti-symmetric\n",
    "        # and all second-order quantities are symmetric.\n",
    "        # We take advantage of this, and average the two halves of\n",
    "        # the domain together to gain more statistics\n",
    "        \n",
    "        # Build arrays taking advantage of the symmetry\n",
    "        n = tmp.shape[0]\n",
    "        if \"bar\" in var:\n",
    "            tmp = np.concatenate((tmp[:n//2,:], -np.flip(tmp[n//2:,:])), axis=1)\n",
    "        else:\n",
    "            tmp = np.concatenate((tmp[:n//2,:], np.flip(tmp[n//2:,:])), axis=1)\n",
    "        \n",
    "        # Record mean and standard deviation (with respect to time)\n",
    "        if n==x.size:\n",
    "            df[vname] = tmp.mean(axis=1)\n",
    "            df[\"σ\"+vname] = tmp.std(axis=1)\n",
    "        elif n==xr.size:\n",
    "            dfr[vname] = tmp.mean(axis=1)\n",
    "            dfr[\"σ\"+vname] = tmp.std(axis=1)\n",
    "    \n",
    "    # Append DataFrames from each individual simulation to the lists\n",
    "    dlst.append(df)\n",
    "    drlst.append(dfr)\n",
    "\n",
    "# Construct DataFrames covering all simulations by putting all data together\n",
    "df = pd.concat(dlst)\n",
    "dfr = pd.concat(drlst)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "bec7cf59-614f-4842-b4b9-31a7fae1a272",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.e-02, 5.e+01, 0.e+00])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Add in a density ratio variable to the DataFrames\n",
    "df[\"Rρ\"] = -df[\"RaT\"]*df[\"Sc\"]/df[\"RaS\"]/df[\"Pr\"]\n",
    "dfr[\"Rρ\"] = -dfr[\"RaT\"]*dfr[\"Sc\"]/dfr[\"RaS\"]/dfr[\"Pr\"]\n",
    "df.Rρ.unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f058eacc-4ab9-42ac-9e47-72b753c646eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Add (dimensionless) diffusivity coefficients to the DataFrames\n",
    "# (noting that for high Pr sims, we have switched T and S for convenience)\n",
    "df[\"ν\"] = ( ((df[\"Rρ\"]==50)*(df[\"Pr\"]/df[\"RaT\"])**0.5).fillna(0) + ((df[\"Rρ\"]!=50).fillna(0)*(df[\"Sc\"]/df[\"RaS\"])**0.5).fillna(0) )\n",
    "df[\"κT\"] = df[\"ν\"]/df[\"Pr\"]\n",
    "df[\"κS\"] = df[\"ν\"]/df[\"Sc\"]\n",
    "dfr[\"ν\"] = ( ((dfr[\"Rρ\"]==50)*(dfr[\"Pr\"]/dfr[\"RaT\"])**0.5).fillna(0) + ((dfr[\"Rρ\"]!=50).fillna(0)*(dfr[\"Sc\"]/dfr[\"RaS\"])**0.5).fillna(0) )\n",
    "dfr[\"κT\"] = dfr[\"ν\"]/dfr[\"Pr\"]\n",
    "dfr[\"κS\"] = dfr[\"ν\"]/dfr[\"Sc\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "54953efd-3826-44e0-b051-23f9dcaaae37",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>RaT</th>\n",
       "      <th>Pr</th>\n",
       "      <th>RaS</th>\n",
       "      <th>Sc</th>\n",
       "      <th>x</th>\n",
       "      <th>Tbar</th>\n",
       "      <th>σTbar</th>\n",
       "      <th>Tp2</th>\n",
       "      <th>σTp2</th>\n",
       "      <th>chiT</th>\n",
       "      <th>...</th>\n",
       "      <th>vzT</th>\n",
       "      <th>σvzT</th>\n",
       "      <th>vzbar</th>\n",
       "      <th>σvzbar</th>\n",
       "      <th>vzp2</th>\n",
       "      <th>σvzp2</th>\n",
       "      <th>Rρ</th>\n",
       "      <th>ν</th>\n",
       "      <th>κT</th>\n",
       "      <th>κS</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <th>0</th>\n",
       "      <td>-20000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>10000000.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.000688</td>\n",
       "      <td>-0.496809</td>\n",
       "      <td>0.000200</td>\n",
       "      <td>0.000003</td>\n",
       "      <td>6.313947e-07</td>\n",
       "      <td>0.028058</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000008</td>\n",
       "      <td>0.000053</td>\n",
       "      <td>0.000016</td>\n",
       "      <td>0.000107</td>\n",
       "      <td>0.000006</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-20000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>10000000.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.002117</td>\n",
       "      <td>-0.490184</td>\n",
       "      <td>0.000614</td>\n",
       "      <td>0.000029</td>\n",
       "      <td>5.973520e-06</td>\n",
       "      <td>0.028057</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000024</td>\n",
       "      <td>0.000161</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.000330</td>\n",
       "      <td>0.000053</td>\n",
       "      <td>0.000012</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0001</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-20000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>10000000.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.003651</td>\n",
       "      <td>-0.483076</td>\n",
       "      <td>0.001057</td>\n",
       "      <td>0.000086</td>\n",
       "      <td>1.775150e-05</td>\n",
       "      <td>0.028047</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000041</td>\n",
       "      <td>0.000272</td>\n",
       "      <td>0.000085</td>\n",
       "      <td>0.000568</td>\n",
       "      <td>0.000153</td>\n",
       "      <td>0.000034</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-20000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>10000000.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.005288</td>\n",
       "      <td>-0.475489</td>\n",
       "      <td>0.001531</td>\n",
       "      <td>0.000181</td>\n",
       "      <td>3.720458e-05</td>\n",
       "      <td>0.028018</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000058</td>\n",
       "      <td>0.000386</td>\n",
       "      <td>0.000124</td>\n",
       "      <td>0.000823</td>\n",
       "      <td>0.000310</td>\n",
       "      <td>0.000068</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-20000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>10000000.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.007029</td>\n",
       "      <td>-0.467427</td>\n",
       "      <td>0.002032</td>\n",
       "      <td>0.000320</td>\n",
       "      <td>6.557969e-05</td>\n",
       "      <td>0.027955</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000076</td>\n",
       "      <td>0.000502</td>\n",
       "      <td>0.000164</td>\n",
       "      <td>0.001093</td>\n",
       "      <td>0.000528</td>\n",
       "      <td>0.000115</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0001</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 37 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       RaT   Pr         RaS    Sc         x      Tbar     σTbar       Tp2  \\\n",
       "0 -20000.0  1.0  10000000.0  10.0  0.000688 -0.496809  0.000200  0.000003   \n",
       "1 -20000.0  1.0  10000000.0  10.0  0.002117 -0.490184  0.000614  0.000029   \n",
       "2 -20000.0  1.0  10000000.0  10.0  0.003651 -0.483076  0.001057  0.000086   \n",
       "3 -20000.0  1.0  10000000.0  10.0  0.005288 -0.475489  0.001531  0.000181   \n",
       "4 -20000.0  1.0  10000000.0  10.0  0.007029 -0.467427  0.002032  0.000320   \n",
       "\n",
       "           σTp2      chiT  ...       vzT      σvzT     vzbar    σvzbar  \\\n",
       "0  6.313947e-07  0.028058  ... -0.000008  0.000053  0.000016  0.000107   \n",
       "1  5.973520e-06  0.028057  ... -0.000024  0.000161  0.000050  0.000330   \n",
       "2  1.775150e-05  0.028047  ... -0.000041  0.000272  0.000085  0.000568   \n",
       "3  3.720458e-05  0.028018  ... -0.000058  0.000386  0.000124  0.000823   \n",
       "4  6.557969e-05  0.027955  ... -0.000076  0.000502  0.000164  0.001093   \n",
       "\n",
       "       vzp2     σvzp2    Rρ      ν     κT      κS  \n",
       "0  0.000006  0.000001  0.02  0.001  0.001  0.0001  \n",
       "1  0.000053  0.000012  0.02  0.001  0.001  0.0001  \n",
       "2  0.000153  0.000034  0.02  0.001  0.001  0.0001  \n",
       "3  0.000310  0.000068  0.02  0.001  0.001  0.0001  \n",
       "4  0.000528  0.000115  0.02  0.001  0.001  0.0001  \n",
       "\n",
       "[5 rows x 37 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Preview the DataFrames\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e9884f27-53c4-410c-a154-15f1bd0af8af",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>RaT</th>\n",
       "      <th>Pr</th>\n",
       "      <th>RaS</th>\n",
       "      <th>Sc</th>\n",
       "      <th>x</th>\n",
       "      <th>Sbar</th>\n",
       "      <th>σSbar</th>\n",
       "      <th>Sp2</th>\n",
       "      <th>σSp2</th>\n",
       "      <th>chiS</th>\n",
       "      <th>...</th>\n",
       "      <th>vxS</th>\n",
       "      <th>σvxS</th>\n",
       "      <th>vyS</th>\n",
       "      <th>σvyS</th>\n",
       "      <th>vzS</th>\n",
       "      <th>σvzS</th>\n",
       "      <th>Rρ</th>\n",
       "      <th>ν</th>\n",
       "      <th>κT</th>\n",
       "      <th>κS</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-20000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>10000000.0</td>\n",
       "      <td>10.0</td>\n",
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       "      <td>0.000100</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>2.160941e-07</td>\n",
       "      <td>0.018790</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.378325e-09</td>\n",
       "      <td>4.226866e-10</td>\n",
       "      <td>-0.002868</td>\n",
       "      <td>0.000145</td>\n",
       "      <td>-0.000005</td>\n",
       "      <td>0.000035</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0001</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-20000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>10000000.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.000592</td>\n",
       "      <td>-0.492577</td>\n",
       "      <td>0.000308</td>\n",
       "      <td>0.000011</td>\n",
       "      <td>2.045367e-06</td>\n",
       "      <td>0.018789</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.635874e-08</td>\n",
       "      <td>4.693058e-09</td>\n",
       "      <td>-0.004093</td>\n",
       "      <td>0.000208</td>\n",
       "      <td>-0.000007</td>\n",
       "      <td>0.000049</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-20000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>10000000.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.001021</td>\n",
       "      <td>-0.487198</td>\n",
       "      <td>0.000531</td>\n",
       "      <td>0.000032</td>\n",
       "      <td>6.083622e-06</td>\n",
       "      <td>0.018788</td>\n",
       "      <td>...</td>\n",
       "      <td>-6.180830e-08</td>\n",
       "      <td>1.767146e-08</td>\n",
       "      <td>-0.006160</td>\n",
       "      <td>0.000318</td>\n",
       "      <td>-0.000011</td>\n",
       "      <td>0.000075</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-20000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>10000000.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.001479</td>\n",
       "      <td>-0.481450</td>\n",
       "      <td>0.000770</td>\n",
       "      <td>0.000066</td>\n",
       "      <td>1.276973e-05</td>\n",
       "      <td>0.018784</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.671903e-07</td>\n",
       "      <td>4.772083e-08</td>\n",
       "      <td>-0.008867</td>\n",
       "      <td>0.000465</td>\n",
       "      <td>-0.000016</td>\n",
       "      <td>0.000109</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-20000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>10000000.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.001966</td>\n",
       "      <td>-0.475333</td>\n",
       "      <td>0.001023</td>\n",
       "      <td>0.000117</td>\n",
       "      <td>2.256594e-05</td>\n",
       "      <td>0.018775</td>\n",
       "      <td>...</td>\n",
       "      <td>-3.758897e-07</td>\n",
       "      <td>1.070555e-07</td>\n",
       "      <td>-0.011744</td>\n",
       "      <td>0.000625</td>\n",
       "      <td>-0.000022</td>\n",
       "      <td>0.000145</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0001</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       RaT   Pr         RaS    Sc         x      Sbar     σSbar       Sp2  \\\n",
       "0 -20000.0  1.0  10000000.0  10.0  0.000192 -0.497587  0.000100  0.000001   \n",
       "1 -20000.0  1.0  10000000.0  10.0  0.000592 -0.492577  0.000308  0.000011   \n",
       "2 -20000.0  1.0  10000000.0  10.0  0.001021 -0.487198  0.000531  0.000032   \n",
       "3 -20000.0  1.0  10000000.0  10.0  0.001479 -0.481450  0.000770  0.000066   \n",
       "4 -20000.0  1.0  10000000.0  10.0  0.001966 -0.475333  0.001023  0.000117   \n",
       "\n",
       "           σSp2      chiS  ...           vxS          σvxS       vyS  \\\n",
       "0  2.160941e-07  0.018790  ... -1.378325e-09  4.226866e-10 -0.002868   \n",
       "1  2.045367e-06  0.018789  ... -1.635874e-08  4.693058e-09 -0.004093   \n",
       "2  6.083622e-06  0.018788  ... -6.180830e-08  1.767146e-08 -0.006160   \n",
       "3  1.276973e-05  0.018784  ... -1.671903e-07  4.772083e-08 -0.008867   \n",
       "4  2.256594e-05  0.018775  ... -3.758897e-07  1.070555e-07 -0.011744   \n",
       "\n",
       "       σvyS       vzS      σvzS    Rρ      ν     κT      κS  \n",
       "0  0.000145 -0.000005  0.000035  0.02  0.001  0.001  0.0001  \n",
       "1  0.000208 -0.000007  0.000049  0.02  0.001  0.001  0.0001  \n",
       "2  0.000318 -0.000011  0.000075  0.02  0.001  0.001  0.0001  \n",
       "3  0.000465 -0.000016  0.000109  0.02  0.001  0.001  0.0001  \n",
       "4  0.000625 -0.000022  0.000145  0.02  0.001  0.001  0.0001  \n",
       "\n",
       "[5 rows x 21 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfr.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "46bd61fa-397b-4b81-ab2a-57fbae62ff4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write the DataFrames to CSV files\n",
    "df.to_csv(\"base_profiles.csv\")\n",
    "dfr.to_csv(\"ref_profiles.csv\")"
   ]
  }
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