demo_numerical_w_figs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating the correlation scale and Taylor scale\n",
    "*Demonstrating the calculation of numerically-derived variables in the Wind database*\n",
    "\n",
    "As well as raw variables such as electron density and magnetic field strength, and analytically-derived variables such as Alfven speed and ion gyroradius, the *Wind* database contains numerically-derived (\"estimated\") variables. The two parameters we are most interested are the *correlation scale* and *Taylor scale*. Both scales are calculated from the autocorrelation function, and both require some thought as to what technique to use to calculate them.\n",
    "\n",
    "### Notes\n",
    "- The interval used to demonstrate the pipeline is not ideal in that its ACF lacks the desired parabolic shape near the origin and overall exponential shape. However, it is still a useful demonstration given that not all ACFs will have this nice shape.\n",
    "- Scales are returned in units of seconds\n",
    "- For demonstration purposes, `plot=True` arguments in functions assume a solar wind speed of 400km/s. The specific speeds measured for each interval are used in the actual analysis. \n",
    "- We expect slight variation from Kevin's numbers due to using a cadence of 11Hz instead of 10Hz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import pandas as pd\n",
    "import importlib\n",
    "\n",
    "# import os\n",
    "# while \".toplevel\" not in os.listdir():\n",
    "#     os.chdir(\"..\")\n",
    "\n",
    "import src.utils as utils\n",
    "import src.params as params\n",
    "\n",
    "sys_arg_dict = {\n",
    "    # arg1\n",
    "    \"mag_path\": params.mag_path,\n",
    "    \"proton_path\": params.proton_path,\n",
    "    \"electron_path\": params.electron_path,\n",
    "    # arg2\n",
    "    \"mag_vars\": [params.timestamp, params.Bwind, params.Bwind_vec],\n",
    "    \"proton_vars\": [params.timestamp, params.np, params.Tp],\n",
    "    \"electron_vars\": [params.timestamp, params.ne, params.Te],\n",
    "    # arg3\n",
    "    \"mag_thresh\": params.mag_thresh,\n",
    "    \"proton_thresh\": params.proton_thresh,\n",
    "    \"electron_thresh\": params.electron_thresh,\n",
    "    # arg4\n",
    "    \"dt_hr\": params.dt_hr,\n",
    "    \"int_size\": params.int_size,\n",
    "    # arg5\n",
    "    \"dt_lr\": params.dt_lr,\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set fontsize of plots (check matches utils.py)\n",
    "plt.rcParams.update({\"font.size\": 9})\n",
    "plt.rc(\"text\", usetex=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'src.utils' from 'c:\\\\Users\\\\spann\\\\Documents\\\\Research\\\\Code repos\\\\reynolds_scales_project\\\\src\\\\utils.py'>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "importlib.reload(utils)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a bash terminal, run `bash 0_download_files.sh`, followed by `bash 1_get_raw_vars.sh`. (For some reason `%%bash` command in a Jupyter cell isn't working)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculating numerically-derived variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 11Hz data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "file = \"data/raw/wind/mfi/mfi_h2/2016/wi_h2_mfi_20160102_v05.cdf\"\n",
    "timestamp = \"2016-01-02 12:00:00\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = utils.pipeline(\n",
    "    file,\n",
    "    varlist=sys_arg_dict[\"mag_vars\"],\n",
    "    thresholds=sys_arg_dict[\"mag_thresh\"],\n",
    "    cadence=sys_arg_dict[\"dt_hr\"],\n",
    ")\n",
    "# print(\"Reading {0}: {1:.2f}% missing\".format(file, df.iloc[:,0].isna().sum()/len(df)*100))\n",
    "\n",
    "# Ensuring observations are in chronological order\n",
    "df_wind_hr = df.sort_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(939131, 4)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# df_wind_hr = pd.read_pickle(\"data/processed/\" + params.mag_path + params.dt_hr + \".pkl\")\n",
    "df_wind_hr = df_wind_hr.rename(\n",
    "    columns={params.Bwind: \"Bwind\", params.Bx: \"Bx\", params.By: \"By\", params.Bz: \"Bz\"}\n",
    ")\n",
    "\n",
    "df_wind_hr.shape"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extracting a single 12-hour interval to demonstrate the pipeline. *The timestamp \"00:00\" refers to data betweeen 00:00 and 12:00.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(469565, 4)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_wind_hr = df_wind_hr[\n",
    "    pd.to_datetime(timestamp) : pd.to_datetime(timestamp)\n",
    "    + pd.to_timedelta(params.int_size)\n",
    "]\n",
    "int_wind_hr.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 469565 entries, 2016-01-02 12:00:00.072000 to 2016-01-02 23:59:59.960000\n",
      "Freq: 92L\n",
      "Data columns (total 4 columns):\n",
      " #   Column  Non-Null Count   Dtype  \n",
      "---  ------  --------------   -----  \n",
      " 0   Bwind   459891 non-null  float32\n",
      " 1   Bx      459891 non-null  float32\n",
      " 2   By      459891 non-null  float32\n",
      " 3   Bz      459891 non-null  float32\n",
      "dtypes: float32(4)\n",
      "memory usage: 10.7 MB\n"
     ]
    }
   ],
   "source": [
    "int_wind_hr.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Bwind    9674\n",
       "Bx       9674\n",
       "By       9674\n",
       "Bz       9674\n",
       "dtype: int64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_wind_hr.isna().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 0.2Hz data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(17280, 4)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# df_wind_lr = pd.read_pickle(\"data/processed/\" + params.mag_path + params.dt_lr + \".pkl\")\n",
    "# df_wind_lr = df_wind_lr.rename(\n",
    "#     columns={\n",
    "#         params.Bwind:'Bwind',\n",
    "#         params.Bx:'Bx',\n",
    "#         params.By:'By',\n",
    "#         params.Bz:'Bz'})\n",
    "\n",
    "df_wind_lr = df_wind_hr.resample(\"5S\").mean()\n",
    "df_wind_lr.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extracting a single interval to demonstrate the pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(8640, 4)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_wind_lr = df_wind_lr[\n",
    "    pd.to_datetime(timestamp) : pd.to_datetime(timestamp)\n",
    "    + pd.to_timedelta(params.int_size)\n",
    "]\n",
    "int_wind_lr.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "int_wind_lr.plot(subplots=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.020602046575021564\n"
     ]
    }
   ],
   "source": [
    "missing = int_wind_hr.iloc[:, 0].isna().sum() / len(int_wind_hr)\n",
    "print(missing)\n",
    "\n",
    "if missing > 0.4:\n",
    "    # Replacing values in lists with na\n",
    "    print(\"Large missing %\")\n",
    "else:\n",
    "    int_wind_hr = int_wind_hr.interpolate().ffill().bfill()\n",
    "    int_wind_lr = int_wind_lr.interpolate().ffill().bfill()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Bwind    0\n",
       "Bx       0\n",
       "By       0\n",
       "Bz       0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_wind_hr.isna().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Bwind    0\n",
       "Bx       0\n",
       "By       0\n",
       "Bz       0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_wind_lr.isna().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Takes ~ 5min\n",
    "\n",
    "# int_wind_hr.plot(subplots=True)\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to fully implement Chuychai's method, we need the spectral index (slope) of the power law in the dissipation range. Here we compute a smoothed 3D periodogram for a single high-res interval, then perform a least squares fit of a power law to the inertial and kinetic ranges to determine their slopes and the spectral break."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Maths for calculating breakpoint:**\n",
    "\n",
    "Each power-law fit is given by the following equation:\n",
    "\n",
    "$$y =x^me^c$$\n",
    "\n",
    "This is because if we take the log of both sides, we get the formula for a straight line on a log-log plot:\n",
    "\n",
    "$$\\log(y) = m\\log(x)+c$$\n",
    "\n",
    "We want to find the x-value for which the two power-laws are equal. We can do this by subtracting one from the other and finding the value of $\\log(x)$ where this subtraction = 0, i.e., the root of the equation.\n",
    "\n",
    "$$m_1\\log(x)+c_1-m_2\\log(x)-c_2=0$$\n",
    "\n",
    "Finally, we take the exponential of this root to get the x-value of the spectral break\n",
    "\n",
    "$$x = e^{\\log(x)}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reading in dataframe to get values for qi, di, etc.\n",
    "df_wind = pd.read_csv(\"wind_dataset.csv\", index_col=\"Timestamp\")\n",
    "df_wind.index = pd.to_datetime(df_wind.index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Re_lt</th>\n",
       "      <th>Re_tb</th>\n",
       "      <th>Re_di</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1.970300e+04</td>\n",
       "      <td>1.839900e+04</td>\n",
       "      <td>1.722500e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.209253e+08</td>\n",
       "      <td>1.316693e+05</td>\n",
       "      <td>3.749882e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>7.841428e+09</td>\n",
       "      <td>2.037565e+05</td>\n",
       "      <td>4.030641e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.255346e+03</td>\n",
       "      <td>3.476500e-01</td>\n",
       "      <td>6.719223e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>8.101501e+05</td>\n",
       "      <td>3.186781e+04</td>\n",
       "      <td>1.398007e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.832300e+06</td>\n",
       "      <td>6.906081e+04</td>\n",
       "      <td>2.506057e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>4.398361e+06</td>\n",
       "      <td>1.471352e+05</td>\n",
       "      <td>4.592258e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>9.272259e+11</td>\n",
       "      <td>3.677702e+06</td>\n",
       "      <td>7.931448e+06</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Re_lt         Re_tb         Re_di\n",
       "count  1.970300e+04  1.839900e+04  1.722500e+04\n",
       "mean   1.209253e+08  1.316693e+05  3.749882e+05\n",
       "std    7.841428e+09  2.037565e+05  4.030641e+05\n",
       "min    1.255346e+03  3.476500e-01  6.719223e+01\n",
       "25%    8.101501e+05  3.186781e+04  1.398007e+05\n",
       "50%    1.832300e+06  6.906081e+04  2.506057e+05\n",
       "75%    4.398361e+06  1.471352e+05  4.592258e+05\n",
       "max    9.272259e+11  3.677702e+06  7.931448e+06"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_wind[[\"Re_lt\", \"Re_tb\", \"Re_di\"]].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Re_lt</th>\n",
       "      <th>Re_tb</th>\n",
       "      <th>Re_di</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Re_lt</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.030710</td>\n",
       "      <td>0.022769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Re_tb</th>\n",
       "      <td>0.030710</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.689551</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Re_di</th>\n",
       "      <td>0.022769</td>\n",
       "      <td>0.689551</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Re_lt     Re_tb     Re_di\n",
       "Re_lt  1.000000  0.030710  0.022769\n",
       "Re_tb  0.030710  1.000000  0.689551\n",
       "Re_di  0.022769  0.689551  1.000000"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_wind[[\"Re_lt\", \"Re_tb\", \"Re_di\"]].corr(\"pearson\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Re_lt</th>\n",
       "      <th>Re_tb</th>\n",
       "      <th>Re_di</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Re_lt</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.461822</td>\n",
       "      <td>0.723722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Re_tb</th>\n",
       "      <td>0.461822</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.744292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Re_di</th>\n",
       "      <td>0.723722</td>\n",
       "      <td>0.744292</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Re_lt     Re_tb     Re_di\n",
       "Re_lt  1.000000  0.461822  0.723722\n",
       "Re_tb  0.461822  1.000000  0.744292\n",
       "Re_di  0.723722  0.744292  1.000000"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_wind[[\"Re_lt\", \"Re_tb\", \"Re_di\"]].corr(\"spearman\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following requires specification of the inertial and kinetic ranges. I have used the values used previously in the literature for Wind spectral analysis. Sometimes we cannot get a good intersection between the two for a spectral break."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'src.utils' from 'c:\\\\Users\\\\spann\\\\Documents\\\\Research\\\\Code repos\\\\reynolds_scales_project\\\\src\\\\utils.py'>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "importlib.reload(utils)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.740423114261999, -3.026077172159704, 0.20382611339664775)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 237.6x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "qi, qk, spectral_break, fig, ax, f_periodogram, p_smooth = utils.compute_spectral_stats(\n",
    "    [int_wind_hr.Bx, int_wind_hr.By, int_wind_hr.Bz],\n",
    "    # dt=float(params.dt_hr[:-1]),\n",
    "    f_min_inertial=params.f_min_inertial,\n",
    "    f_max_inertial=params.f_max_inertial,\n",
    "    f_min_kinetic=params.f_min_kinetic,\n",
    "    f_max_kinetic=params.f_max_kinetic,\n",
    "    timestamp=timestamp,\n",
    "    di=df_wind.loc[timestamp, \"dp\"],\n",
    "    velocity=df_wind.loc[timestamp, \"V0\"],\n",
    "    plot=True,\n",
    ")\n",
    "\n",
    "qi, qk, spectral_break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fig.savefig(\"plots/final/spectrum_annotated.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- $\\alpha_{i}=-1.66$\n",
    "- $\\alpha_{k}=-2.4$\n",
    "- $f_d=0.26$ Hz (dissipation scale)\n",
    "- $\\tau_d=1/f_d=1/0.26=3.8$\n",
    "\n",
    "Chuychai et al. recommend that the resolution of the data be at least as good as $\\Delta t <0.4\\tau_d$. We later find the mean value of $\\tau_d$ to be $1/0.25=4$. Using this value, we see our resolution is sufficient:\n",
    "\n",
    "- $1/11 = 0.091$\n",
    "- $0.4\\times4=1.6$\n",
    "- $0.091 < 1.6$\n",
    "\n",
    "<u>We need to justify the frequency bounds we have specified for fitting the power law slopes.</u>\n",
    "See e.g. *The kinetic range is usually above the spacecraft frame frequency corresponding to the proton inertial length, $f_{pi}=v_{SW}/(2\\pi\\lambda_{pi}$)* (from Pitna et al. (2021), quantities plotted as vertical lines above)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ACF function\n",
    "\n",
    "This is what we use to calculate the correlation scale and Taylor scale. Note that Chuychai et al. did not calculate the ACF directly from the data; they calculated it from the second-order structure function. Here, we will calculate it directly from the data.\n",
    "\n",
    "The following function is based off Kevin's `compute_corr.compute_correlation_time_scale.compute_autocorrelation_function()`. It automatically detects whether being fed 1D (scalar) or 3D time series, for which the calculation is as follows:\n",
    "\n",
    "$$R(\\tau)=\\frac{1}{3}\\times(R_{xx}(\\tau)+R_{yy}(\\tau)+R_{zz}(\\tau))$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following low-cadence, high $r$ ACF will be used for calculating the outer scale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'src.utils' from 'c:\\\\Users\\\\spann\\\\Documents\\\\Research\\\\Code repos\\\\reynolds_scales_project\\\\src\\\\utils.py'>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "importlib.reload(utils)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "time_lags_lr, r_vec_lr = utils.compute_nd_acf(\n",
    "    [int_wind_lr.Bx, int_wind_lr.By, int_wind_lr.Bz],\n",
    "    nlags=params.nlags_lr,\n",
    "    plot=True,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following high-cadence, low $r$ ACF will be used for calculating the Taylor scale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "time_lags_hr, r_vec_hr = utils.compute_nd_acf(\n",
    "    [int_wind_hr.Bx, int_wind_hr.By, int_wind_hr.Bz],\n",
    "    nlags=params.nlags_hr,\n",
    "    plot=True,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlation scale functions\n",
    "\n",
    "Names for $\\tau_c$:\n",
    "- Outer scale\n",
    "- (Longitudinal) integral scale\n",
    "- Correlation scale\n",
    "\n",
    "Methods for calculating:\n",
    "- 1/e trick\n",
    "- Exponential fit\n",
    "- Integration\n",
    "\n",
    "Smith et al. (2001) used the 1/e trick method (which they call $e$-folding) and the integration method. In Appendix B of their paper, they show how the estimates by either method increase depending on the lag up to which you calculate the ACF."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Firstly, using Kevin's function (just with plotting functionality added) for computing outer scale using $1/e$ trick:\n",
    "\n",
    "**If we set $f(\\tau)=\\exp(-\\tau/\\tau_c)=e^{-1}$, then $\\tau_c=\\tau$.**\n",
    "\n",
    "Kevin referred to the value calculated from this method in his analysis as `estimate` and `Correlation_timescale_est`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'src.utils' from 'c:\\\\Users\\\\spann\\\\Documents\\\\Research\\\\Code repos\\\\reynolds_scales_project\\\\src\\\\utils.py'>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "importlib.reload(utils)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1129.727"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 237.6x180 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tce, fig, ax = utils.compute_outer_scale_exp_trick(time_lags_lr, r_vec_lr, plot=True)\n",
    "tce"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What values should we expect? The lit review spreadsheet shows values in the range of $\\lambda_C=$ 320,000 - 1,200,000km.\n",
    "\n",
    "Secondly, adapting Kevin's function for computing outer scale using exponential fit, from `compute_correlation_time_scale()`. A function of the following form is fit to the ACF $R(\\tau)$.\n",
    "\n",
    "$$f(\\tau)=\\exp(-\\tau/\\tau_c)$$\n",
    "\n",
    "\n",
    "Kevin referred to the value calculated from this method as `lambda_c` and `Correlation_timescale`.\n",
    "\n",
    "<u>How to choose how much of the ACF to fit to?</u> Kevin used 1000 seconds, which was decided \"through some trial and error and inspection of plotted results\". While we should keep in mind that the correlation length will tend to increase with the maximum lag we fit to, I think we should fit to much more than 1000 seconds, as in the literature we see typical fits to 1-3,000,000km, corresponding to 2500-7500 seconds or 500-1500 lags. **We are now fitting to 2 times the correlation timescale, as estimated by the 1/e method.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Fit to 2 * 1/e estimate**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1085.4295087027403"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tcf, fig, ax = utils.compute_outer_scale_exp_fit(\n",
    "    time_lags=time_lags_lr,\n",
    "    acf=r_vec_lr,\n",
    "    seconds_to_fit=np.round(2 * tce),\n",
    "    fig=fig,\n",
    "    ax=ax,\n",
    "    plot=True,\n",
    ")\n",
    "tcf\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, creating a function for computing outer scale as integral of the ACF. This formula comes from the re-arrangement of the simple exponential that a time series follows if it approximates a Markov process (Batchelor, 1970). \n",
    "\n",
    "$$\\tau_C=\\int_0^\\infty R(\\tau)d\\tau$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1380.5474687085905"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tci, fig, ax = utils.compute_outer_scale_integral(\n",
    "    time_lags_lr, r_vec_lr, fig=fig, ax=ax, plot=True\n",
    ")\n",
    "tci\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 237.6x180 with 1 Axes>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig.savefig(\"plots/final/corr_scale_methods.pdf\")"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
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AyiCIGKa6x1XCtPmIjwsvvNB7d1MefPBBc/jhh9t1zgMrDNC7f+ihh+w6sB+ECSk/zZs3ty6bV1991QwfPtxst912ZsqUKd67G0Ol4EQHYClxoqN+/fr21eEsDbwGzyHobvHDewSjJnKbJAPn5BcjbHMObgK6XFRuQojE8IxW1lVcIeI9L1EgFNKEb47rr7++dOI3YD0uVOz6AQccEGvXrp1dX7NmTWyrrbaKrV27NjZ79uxYhw4dbHmyPPPMM7F4rzz20UcfeSUbuPjii2MXXHCBXa9du7Z9hbp169rz+fDDD2Nx0RA75JBD7L7xxjYWf5i9vcon/vDHrrnmmo1+p4OJ3dzkbbz6J4XzT/LmX/dPOhecSC6I/3Ps558oLi5GvLWS9xx8hknlHHzGvw0cc9iwYXadc4iLD7suhMg+1Aluokk/1JPBySM14ZtImkLLSIoKJ9V5vDG328RVAEGdrMcb6Y0ma8Ny8dxzz5l4Y2fefvtts9tuu3nvVB6mzR86dOhGI1wYOcMwV8pOPvlk06dPH3PCCSfYETeJAl4rAq4mrCr0THBh+C0KmEidlcHv3uAzlPOKpSTMJYIlwllE2MdZI/zrznrC9wOWKf9neJ//A4sfd75uCbpuhBDZg2eWZ9JvNU2EJnwTSaM06OXDg0eAZCL8IqYsiFVgDhj3ituDR+nEE0+0rpvevXuXzhHjB5GSaFQNLo4wd1PUCRMdQojc4IS+6zA4GI2WjAtVokMkjURH9vjpp5/MtttuW2r5YNjtNttsY1588UVTvXp106xZMxsvUuhgaaFyKytmRAiReehM8TyydOvWrcJxVBIdImkkOkS2wXIU7FEJIbIDbhMnNrBuOHCnEsBdETThmxAiIf6KJhdIcAiRGxD8uHexaLh6gBF7jBhbtGiR3Y4iEh1CBOBhdvjXge1EGUQpD+7vh14JwbFl7ZMqlRnmKoTIXxD8uFEYOk8sGkKjrMDxqCDRIUQAknYRGEqcgt+SgAmTh5rehD8KnH0IpKQcYcF+YRAkSsWQLtHBcWRpEKI4cPMs+aHTQT1A/ZMvdYFEhyh4GNrKcNdkoddAqBMCwx8gyQPuhqxS7gK1eGWbcsRIWQl30lkxIG40FFWI4oD6hTrJT5QtGomQ6ChyXM4FP6mUBcvDyiDZMgfWBjfPyMMPP5xUuvJEkEGUkSaHHXaYOeuss8zixYu9d8LBcsHD7X/Agw87IsOV8Tv8Dz8ZRsuD3gnixFlFEC70ZNhm3V1HlkSWE87T/71uf7lchMhPqBfuvvvu0PmoqB/yUWQEkegocsLiE8J66snMhOpI9piJLAI0nAiFjz/+2G7Xrl07YW6LZCEamzlXLr30UnPooYeaffbZx7z88sveuxvDg+1cKy7/hN/N4nCio6z3ygJfrLNU8Iq4wAWDtQTBhVWEbURE8Ds4vt8Kw2fZh/395UKI6MMIFKZ9oLOFuKAOdJZUB/VSIbhTJTpEJCHHhRvyxfq7775r1ysL2U2Zl+WTTz4xV111lRkyZIj3zgac0KABr6irpKyGH4HAd/jjQlyF4noywXiNoIihUvK7Vvg+Kisqri+//NIrFUJEGeqBWrVq2brAb9EkQLRQOw8SHSJy0Ni/9dZbpl27dnb7vvvuM+PHj7frLvU4MMkbjbOjb9++3lpiCOTs3r27Ofvss206ddKb+8Gq4ESHH86JqfAdflEQrBz85xSGM5MiHCpK0PLBd7IQj0Im1GQsLUKI3EId4p5lMhL7J0iU6BBm9uzZ5pZbbrH+th133NGOcMBEzjaBip9++qm3Z/7AjR4kLBV42H6JSPaYYWWOuXPnlsZGIEAQGMzISnpxHtK9997bPPDAA9Ysyf9h+fLldtr3REybNs36Su+//35zySWXmMcee8y0bdvWe3cDiAtEASAKOnToYNeB0SmugqBRd5YKfy+Fhr+s4E7eR3AgbFjc8YIioiz4ruB3cK4sVFRlfb8QIjdQZwSfc+oO5oqiM8Tzy7azdhYqykiaBD/88IO55pprTN26dc0BBxxgF6Zbd6xatcosXLiwdGKy1atX25TY2abQMpIiJsDdosR1ID4wR44bN85OrsZ7bt6TF154wc59EoTp8Hv27Gm6dOlixWJ58PBTQfDwO2EBVBg0+JSzIFAcrtyJjrCKwwkD4LjOZ+sECHBMZ7WgF8TiPuP2wRrjhJHD7QOcp4SHENGCZ5pn3j3HUSXTGUmprEUZxG+QWLyHG5s6dapXUjZvvvmmnQacz2WbQpza3sGU83HBYddv8KaNjzfI9pXbmOud6HZm6vlCgemp3ZTxQohoMm/ePLsEyYdnV1Pb5ynxRtL2yrNJscy98vzzz5s2bdqYFStWmB122MH2HHB9FEPvnp4S1hAXTyKEiAZYMp5++mlriWQd16w/ODRf0IRveQLmbb+5PRdowrfCB9dJmOtGCJF9eB4RGnQG/C5OIN4P8ZFvaMK3CMK05txg/iVRzgcRbYKBXWGwTzL7ZQMJDiGiBaPmnOAg+J3hrpMnT85LwZENZOmoAGS2JHeEHxqlskZPZINCsXTwAOMycUGVmChd4CQ9irIeZv4PyTTMHIPjO3dFWfDduDOCwZtCCEFQOPUO7t1EQeT5hAJJI8Z7770Xmzlzpre1gVwEjgYplEDS6dOn24BJt05grmP06NHeWjjlve+H43L88oj3XGIHHXSQtyWEKFaoCwqdTAeSyr2SIgyXDVOADKcV6aEsa4VLmMM+pFvn1YH1glwcQShPJY27H4bOYnUhYU9ZFpYw+E7/Z1h3i/+82S8smRf7uPLgb6U87DNCiMyBVdS5UkTFkHulApAjgkbgjDPO8EpKkk+R4TKXVMS9UtHGON0kSj7mXC3+Bx2XCKIEUyYuD8ybiBEaYdaJHud9ylz0OJUF7/mjySlzbpxEuJwYYS4WjsUcKbjVeI/ju3NhPz7LPu5c2eZ3sM4rv4O05fh/WUdUuOPzPos7Ju+D+x53LASM/5yEEJWHpIM8Y2T3zXd3SarIvRIxVq9eHTv66KNLl3iDVbrkmoq4V7gFcr00a9bMO5tNCbpXgLwpDtwwHTp08LZKXCZ++LwbL9+3b9+N3CnJuFecu4ZjxBt8u+4Hc6s7flw82FfG4g8aNMiugzsnvst/ruAft+8/dz7vzs1fzvmEHVsIUTmoS3CT85y7uikVd22hIPdKxJgzZ4658MILrWWDJd4w2KWs3rJIH1gD/D0P1hmyFsS5IngfKwFWAb97IhmclcJ9Nv68bOLScFYHyv2uH3DWCt53uH0czOfizs8P95P7vP8zzj3j3sNSI4SoODyvTOzIDK88TzxfEBf0yoeTASQ6UoQbkdlJg+RrTAdzluR6efHFF72zKR9EgF88UEH450dxOHGA6yHoQkk2FoJj4wrhsyysOzeHg3KOx+IqKEQC5+g+5xdJfvgMcy44l4wrc6+cO8f0ixaO517LOrYQIjmceHf1CkNe3Vwo7nkT6WPz+MVWVykFuBGZoOe7776zE8ARE8EyevRoc9FFF3l75YYbb7zRXHvttd5Wcmy55ZaRWMKggafhZyr6devW2UqBRrh58+Z24jasBMTX0CjXqFHD+1RJnArbjRo1sp9nGnuOQdmsWbNsRUKjzv+SaeARE0H69etnLR0cg+/kOHyWz/EZf2XEubn9gPUFCxbY72SBOnXqlE6TTxkig89xDswlQxnfwTnyHq+IDsrd73PfwXXgc3ye9ykXQlQMnh+e9c6dO9v6hE5AMYt5JsNkHrFMZdRWIGmK0DAcc8wxZrfddjO77rqr2Xnnne3kbpMmTTIffviht1duUEbSwsEfPAoIIypGIUTFof7muVJfu4Rly5aZ2rVre1slKCNpxNhpp53MHXfcYXuaY8aMMXfeeacdtcJ06UKkCywaztVCRemsKEKIiuMshc6VUmxgY3jzzTdNnz59rNjo3bu39072kOhIETKRMslYkCVLlnhrQlQeemL+IFZ/XIcQomx4ZnBnhg0np6zY3Cd0YK644gorulq2bGnuvfdeGyIwdepUs3btWm+v7CDRUQEeffRRb62EsWPH2sZBiHRCBUHsiH/0ihAiMVgF/SNRSBZImZ9isRq+99579lrsvffepmnTptZC/9VXX9n36Dhj7SCIP1FMXaaQ6KgABI26Cd74p/bo0cOuZ5rHH3/cJqM6+uijzYABA7xSIYQobhAW1I1ObDj3CSNRioU//vjDBtH379/f7LHHHrazwrX47LPP7PtMRkesGEKDWI7hw4ebv/zlL/a9bKJA0gpCLMfMmTPtjLNkrwsG46QbxM1bb71lbr75Zrt99dVXmxYtWphBgwbZbVAgqRCiGKExpR4GGldcKJQVg1WDPEVPPvmkefbZZzeJVcGK0a5dO3PWWWfZ7MfJoEDSiIKaPPLII634QHAgAjIJSv7AAw+0Q5lYEBxCCCFKYqAQG3TCqCvZLlTBQcfymWeeMWeeeaaNMWRkG4ManOCgPerZs2epCJk4cWLSgiMbyNKRBFWqVPHWEoPvncyk2QI/XZcuXTaydFSrVm2TYbv77LOPtyaEEPkPQ15dvFOxgOuE9uWJJ54wTz311CYWjb322suKD5YjjjgiqTbLQR4jP+edd561FGXK0iHRkQTETwwZMsTbCgf3h18AZJLTTz/d3oSY1PxUrVrVXHnlld6WsX49biAhhCgkgnlsChVc+OPHjzcTJkwoTTTo2HPPPc3ZZ59trRhNmjTxSlPngw8+sN/hYGAEQacSHcKC4MB8+M4773glG1BMhxCiUKCeozPH1BOIDD+8V6juk/fff99aNMiOyu/0g+WaNoClcePGXml6yXRMh0RHHsGNVrNmTTNq1CivZGMkOoQQ+Q7pBxjq6jLwIi6YC6WQ4fdhYUBszJ8/3ystAYuGExrE9WUaiQ5hueyyy+xcI9wQCIsVK1bYRaNXhBCFAKMwSILnz3nkRqIUYkKvb7/91lozEBrM4+WHob80+meccYY5+OCDvdLsINEhLJgZw5DoEEIUAlg0mEwR6tevb0egBN0q+Q4dRUaTIDRef/11G5vn2H333UuFxqGHHuqVZh+JDpE0Eh1CiHyFwFAWhEYhiQ1yOU2ePNlaNV566SXz22+/ee8YU69ePdu44zph1EkUyLToUJ4OIYQQWQV3SXDYJ0ID10qhCA5+Cw33tttua8455xw7zwmCg0lD+f1YOr7++mszbNiwjAkOAlH79evnbUUDiY4EzJkzx5x88sn2xpk1a5aNFMa/GKUkK0IIkY+QT8IFihYS69evt3NzMdcJ01W4tAY777yzueiii2x7QgpyhAYTr2UChAaBuJwDsSHEyUTpWkt0JKBZs2Y2qxsJaMg2OmLECLNw4UKbgCuVxCtCCFGs0MjS+AaHflKvFlJyr+XLl5t//OMfZrfddrPzvTCrK7Ru3dpaOBAazOzK8N9MtR8ICyc0sKS4c6CzHLQq5RKJjgSsXLnSpjgH0o7zgGAWQ0EWUyY8IYRIFeZBcb19hAdBoUEKIc8GFnEmmttxxx1tUD/iAjp06GDeffdd8+qrr5o2bdrYskyDsPALDcQPsSSUR8llJdGRAIZnIS5QpWQj3Xfffc3+++9vH55spjsXQoh8gMaNThk9bRo51wAyEqWQOmpYvG+88UbbJmARd5lRsYIjQBYsWGCtDryXLrAUIeTKysKKy8ovNNiXsqih0StJ8MUXX1jLB2nFa9Wq5ZVGD41eEULkChpGBIcDVwKdtEIQHKQgf/zxx0NzajDpGq74Sy+91Oy6665eaeVBZCBesBT53SOZbrI1ZDZizJgxwyp4bgKsIQcddJB9uKKARIcQIpfQs6ZeJKaAujGfoaPpcmq89tprG+XU2GabbUz79u1tw9y2bVtTo0YN75304M9Z4oe2BgtGJl1TEh0RgX80UcBhWfFQ+LyXa1OWRIcQIltgxQiL1chnfv75Z5sZFasGOTUYjeJg6KtfaFSvXt17J/3gnsLSQdpz1hFw2bIYSXREAEQFJq6ygnFQ9jyAuUzVK9EhhMgW1Hd0tPLdokGd+fzzz1uLxpQpU8yaNWu8d4yd6+qkk06yDfCJJ56YNqHhrOWJhIQb7ZOLYFuJjgiA4ChPZXKTsOTSfynRIYTIBDSSQXHh4gxy2dGqKGvXrjUvvPCCtWoQeLlq1SrvnRKLRqdOnexCrqZ0QfvggkFZZ4RLFHOVKCNpBEBtEpWdCB4+3CuFEDAlhBAOl2eD4a/BkROIjXwSHMRojB492lpndthhBysqEAEIDoaYkjUUSwc5N/it6RActA3+RF1Yh5wVg2tbjMjSkSQoUlwo/uhsB9MS836uzYyydAgh0gGNMR0pN+wVGI4ZFB5Rh2DMp556yjzzzDN2EIAfRp0gLLp27WpjNDIFwowZwgFxg+hxSxSReyViOF+cMzdyQ0XFpynRIYSoDPTCgxlE823G1++++85MmDDBxmi89dZbGw0x3WqrrWwwKDO58kqdmWnorNJmRFlo+JHoEEkj0SGEqCxuuGY+5dnAkoBFA6FB8sbff//de6ekXiQItHPnzjaOAuGRDhBmxIRg/enbt2/eiLLyUExHnlCs/jkhRP4SVm/hVqHhTiaAPtcgMhASWJy7d+9uXnnllVLBwbwnI0eOtJYPxMGZZ55ZacGBxQLXU3COkygGhEYViY404TdHCiFEPhAWo4ELIMpig8DPoUOHWrfPWWedZeM1HIcddpidwXXJkiV23pMePXrYOIp0gLggIzUWDX+sC6InH9wmUUHulSRAUJBTvyy4sXOtduVeEUIkgnosmPcBa0aU4tLKgvNHbDAChSRejoYNG9ogVwQI65nEBYU6ocFCWSGhmI6IgBmtLDWL8mWfXCLRIYQI4h+Jwki7XCScqgxvvvmmtV7QqfPHahBz0q9fPzsCJV3TxXOtnLsmDESaG0BQqCimIyJwk2FyTLQIIUSUoIEk9sDvDgiL4YgiiKObb77ZNG7c2LRs2dIGiSI4mMm1S5cuZu7cufa3IBAqKziI98CS7VwnZVmsqesLWXBkBSwdojCIP5DemhCiWJk3b14s3jhiwS5dWrVqFZs+fbq3RzRZtmxZ7K677oodfvjhG507S1wQxK644orYN9984+1dOSZPnhw76KCDNvkelr59+3p7FSfHHntsbMKECd5W+pGlQwghCghGWDiLBhOGRXkkCvERxGjEGzpTu3Zt66J+++23vXeNadeunRk7dqz5+uuvzW233Wbq1q3rvVM5sFb4g0G5TrhwsLDgihKZQzEd5UDwEg9xKoFWPOD4TbPtO1VMhxACaLyps6KaO2LhwoW2kSeGwh8Uutlmm5mjjjrKBoWeeuqp1uWRKm5Ya1kCgn3IQcI1QozlW5xLJlEgaQTAx/fee+/ZBDBl+fMQKOzLPrl42CU6hCguaDxpWGlA8wGGsSI2pk6dulGm0GbNmlmhQS6NOnXqeKXJw3UgNoP61x+TkY+Bs7lGoiMiICh4sMnUFzRTcsNzcyM22CdXN7lEhxDFB3UOnZyoNq6//PKLdZEgjj744AOv1Nhp4hEZ/fv3N02aNPFKUwerTtiEnASZ8p0SHakh0RFBcJ8gQlgwz3FTp+J+yRQSHUIUNsQhBOsaOj0sUWtc33nnHTN+/Hjz2GOPme+//94rNWbHHXc0F154oenTp4/ZeeedvdKK4xcdhZw/I1tIdIikkegQojChg0NOClwHBIZGMSgUPv30UzNmzBibnpy4DT8HHHCAFQgMeaWuSgV+fyJRhRCjI4jQkFWj8kh0iKSR6BCisKCxveGGGzZKV05SLDc6JQosXrzYPP7441ZoEPvmZ5tttrEBoUwff8wxx3ilyYGYwIKB0EJMzJs3z3tHZBKJDpE0Eh1CFAZ+y4aDqRaIUYjCiBSajeeee84GhU6bNs0rLaFGjRp22njiNRjySuxGsiA0GHnC7+Ya+FFQaHaQ6BBJI9EhRGHgYjTIY4HYwC3Bkus4hbVr15amVf/kk0+8UmOqVq1qc20gNDp16mQtHBWB30ywvoNJ3XCbILSiEDdXDEh0iKSR6BAiPwkLEKVhz9Xw+yBLly41w4cPNw888IBZvny5V2rMLrvsYsXQeeedZwNEKwvHwsohoZE7JDryBHyuua4cJDqEyE+oO8Kmmc81BK1i2WDxgxhgqOvZZ5/tlZSPc52Q/TMKQkqEI9ERQVDiwYCplStX2p5JLpHoECI/QXDQkEehZ08acoJCJ0yYYJYsWeKVlmQLPemkk6zYIGtoMhCXQdIufh+iA/iNCgqNLpkWHZp7JUV4iHiA8DUSRe4WfLBCCFEWjDph5tdgfZFrVwKdqCuvvNI0aNDANG/e3I4acYJjhx12sHk1GA5LhysZwcHvY+ZWjofLxAkO4lOwdIgiBkuHSB5maly0aJG3tYEozOCoWWaFiCbBmV8HDRrkvZM7Vq9eHRs8eHBs7733Lj0vt9SsWTPWvXv32IsvvujtnTrxjpk9VlxoxLp162ZndhXRR7PMRgyS8oSNkQ8O7xJCCOoFevxYN1y9gWU0l8m9CArFqrHrrruayy67zFowYOutt7ajT3CHkEF01KhR5vjjj7fvVQQsHAypddZhgkOFUExHEvDw+GM4MB26IW0OzIb+MfW5QDEdQkQHGlvcCw5csm6elFxAhtDBgwebBx980CspAQHUs2dP07FjR7Plllt6peWDy4R6MKrZUUXFUCBpBKCSKK+iQHAokFQI4YcGmcaZjkuuZoJ94403zB133GGeffbZ0pldqSs6d+5sBgwYkNJka24ECvUdokpBoYWHREcEQM2Xl5SHBzDX2fIkOoTIHTTIwWBQ6gXqjmwn9aJaRxggNmbNmuWVlgSFXnDBBXaytVSmkHfZUfk9frDe4DZSptDCQaNXIkCwwkCEOHgIZ8yYkfVKRQgRLYhbCDbKNMbZrBuYRh73yT777GMzgzrB0ahRI3P//ffbeVJuuummlAQHTJ48ufS34Uru27evtXBQJsEhUkGiowK44V/AA0dgWK7jOYQQuQX3Sa7qAdKl33zzzWb33Xc3vXr1Mp999pktZ5I13Crz58+35anEbPjht3Xr1s2KDzpduJKjkFNE5B9yryQJQoMH260HHzgeRsV0CFH40Ltn5lca4VwHUc6ZM8dOJU96cuZFcZCW/NJLLzX77befV5IYF6NB/oxcxZ2I6KCYjoiA0GBxwiJoMiVQLNdDwiQ6hMgcTmzgRgEEB2nCsw2jUMaOHWuzhvonXWPuE5J4XXzxxWannXbySsPBWkECMOoz5y7GastMrqK4keiIGFQ8LFEcJibRIUT6CWugiWvAKkBnIxt8++235vHHH7dCY+7cuV5pCbhQzjjjDDvsNRnIG+KEk6NDhw6lk6yJ4kaiQySNRIcQ6QWRgSvVTbeO2EBosGQjQBTXx8iRI82bb77plZRw+OGH20ReDHutXbu2V5ocWDTc78FFhHhSMKhwaPRKxMD3GRa74eI86C243pAQIr9BWLje/6BBg6yVk0Y6k4JjxYoVdoRJ3bp17Xc7wdG4cWMbLMo5MCqFESSpCg6g/uK3MEklFg8JDpFNZOlIER54xqWTKhiRwYNPBUSaY4JJWUeY5MJMKUuHEJUjLEicTgRLphtn4jPIGPrQQw95JcbUqFHDnHPOOTZWI3heYXCe1E1U63KViIogS0fEQFQgOjBLkhjHWT14yKmUMtkDEkJkFkRHcG4lnulMCo7nnnvOtG7d2ubScIIDKwfWjq+//tqOTClLcCA0cMOQxrxWrVpWbBDwKkQUkehIESolzKsu6MoFlPrFhoSHEPkJz3RQdGQCLJIIjH333de0b9++dBRMs2bN7MgUYi6uueYam0G0LAgKdULDnyOE4a9y84ooItGRIvQ4EB1kIfXPQeByeADbQohow7MbHMUBPN+ZgnpiyJAhNolXjx49zIIFC2w52UOZI+Xdd981Z511lqlataotLw//EFdGoIwePdrGavDb1PkRUUQxHRWAnhBuFR5qLB5YP7B4UIHRu+C9XARnKaZDiPKhU4CFgOeYZ5iGO9MNNG6SoUOH2unif/rpJ1tGdlAsFEy6tscee9iyVEFcUP9kazSNKHw0ZDZPoAJzMR25evglOoQoG/JtYMlwrgemMMjkCI4PPvjA3HbbbWbChAnmt99+s2Uk8erdu7dN4lWe+wSBxBLFvECiMJHoiCBUAkSI+32mmDTDhtJmE4kOIcLBGoB1g1fIdHKvl19+2Y5E4dWBNaN///42RXlZc6BQr1C/YMVwbhLqFyGygUavRAwqBFwqVALoNbf4BYgQIlrQUXCCg9gHttMtOH7//XcbBMrw+eOPP75UcBx66KHW0sEkbFg4EgmO4AgUBAdQt2QjuFWIbCBLR4o4N0rQHIuJloqiMjAbJBM4kbgnjLCKx292laVDiMQgMnhe6DSkkzVr1tjp5IcNG2a++uorW1alShXTtm1bc9lll1kXTjJwXlg4HC41OYviNUS2kKUjYjB6JVO9DqaeLgsSBDH+3i2MoBFCbIqzEvjB/ZlOwcF8KJdffrmpV6+e6devnxUcCH86Hx9//LHtRCQrOIBzY6gr4sWNQOFYEhyikJClI0Uwy9LgY/L0J+ypTEzHK6+8Yrp27WpFBYRZOr7//nubBnnZsmVeyabI0iFECVg1WDIRIEpacgJSJ02aZF0qQIwInQbER506dWxZGLh4ksksKkSukKUjYiA6GGJHjwS95pbKQCU2c+ZMbyucjz76yEa9T5kyxYqecePGee8IIYIQJMqzmi7Wr19v4zWIz2jZsqWZOHGiFRwEh9LZYEjs7bffHio46KDwzBKrcfTRRyv+SxQ1snRUACqzYA8Kl0tlh7VRMUGYpeO+++6zC8PsFi9ebCd+Iouh/ztJKMTMkw4qOCLlhShUaMCxOuDGyMSw0tWrV1t3x4gRI6y10XHUUUeZSy65xJxyyileyaY4qyhuEr/QCD63QuQShnXfcccd3pYxr776qn2mMmXpoJcuKsC8efPsAosWLbKvlSXeO7NLMlx55ZWxLl26eFslVKtWLbZmzZqNFiEKlXjjHYuLfzpNsYMOOsgrTQ+///577MEHH4ztvPPO9vgsW2yxReycc86JzZ0719srMfGOQ+nn3NKtW7e01RVCpItgm9G6devYhAkTvHfTj9wrFYDx/phv/cFqYYFr6QRLyqeffuptlQzDw48chOF4/kWIQgOrAc8gljznQsHSkS63Bc9akyZNrF/7u+++s2VXXHGFnQ+FYa0MiS0PF7fBM6pp5EWUCbYZm22WWVkg0ZEiBIIxwywiw5lIM1WRUPm5kTJEwxOohomX5cUXX8yc+UuIiEKj36BBg9I5U4itwl1BXEVlR3l88cUXdg4UxMz8+fNt2emnn26FDVlFywoQDcJIFOZB4bN0UDQCRYgSJDpShN5UWPS563GlGxfnwcgWgtaOOOIIa+VA6MgvLIoNgridRQMLAp2Ayj4HxG1gyWDG18mTJ9syxAwTsI0fP97Ur1/flvnhHHg2y7KuaLirEJuiQNIKQGVC5kCEBgIEa0RlhsymCw2ZFcUAzx/Wg8paGJcuXWoD5h544AH7/MIuu+xibrnlFmvNJMFXEJ55xIaztBBkmqlU6kLkAg2ZjSBUeJhOqWyonNBtuRYcQhQaNPAudbmfysZGEK1/9tln2+nlcZsgOGrUqGGuvvpqm6ocURMUHHQsiCPxu3aI10hXHIkQxYIsHZWACvHHH3+05tcoBIjJ0iEKDQRAOuI1qObIcYNlwsVJwfbbb2/69Olj+vbta9fDYH/iPByIDZd8TO4TUWholtmIQ2+Myoc5E3J9KSU6RKHhYqUqI+rJb3PnnXeazz//3CsxNih0wIAB5oILLjBbb721V5oY9/1YOTUXiihk5F6JOFRGjGQh8EwIUTFwU+C+CLoreL4qIjhWrVpVOuKEmV2d4Nhzzz3t5GzMk3LppZcmJTgAawcCSMGhQlQOiY4kSMZvq5EkQlQMgjldrATCozIQHMr8J3Xr1jVXXXVV6VxFdAqeeOIJG7PRs2dPU61aNVsOiAm+t6y4rMpYWoQQG5DoSIKwYLYg6v0IkRo09sRK4J5E2BMrkcqsrH7IsYFJGHGAePj5559tkqOTTz7Z5vHgGe7cubO3dwlYLxiF5gQP4keIQobnLJlOdCZRTEcS4McNGz7nhwqMyi2XKKZD5AsMO+W5ciA2KjIqBcsFFo2nnnrKKzHWZYLlAosHuW2CkGAMYeLvTCg4VBQatElBC7zfTZgIxXREBJIGISoSLfPmzfP2FEKUh3teaOx5tqgMUxEcjBpDIOy///6lgoPPDx061Hz77bdm+PDhoYIDXFIxYOQZw9/p/SGCJDhEocA97gKxHYiQYFnWwdIhyiZeKXpriWGCp1zDhG9C5ANMfMYEaCtXrvRKkicuKGLbb789Flq71KtXLzZmzBjv3fKJi4xYq1at7IRxQhQCffv29dY2wISkw4YN87Y2wHNXFscee6wmfMs1yQSJlmWuEqKYcSZdP1glcKekYlmYOnWqTVV+8cUXmxUrVpitttrKumkWLlxounTp4u1VPjyrYaZnIaJGWDwhFrlgXAb3cnDSUbJlh1k1/G7NXCDRkQTJVIyp+qKFKBao/HCFVBQmXzv++ONNu3btzIIFC2xZ165dbTzHddddZ7OJOhATBKcSHCpEPhE2U3nYiCqep6AYQXRw7wcJ+3yu2yqJDiFERkG007tK1Zf8ww8/mIsuusgccMAB5uWXX7Zlhx9+uJk9e7Z57LHH7LBYB8GhiA0WZ1lx6cqFiBJYKcKehTDRgEAIWjV4noKfp4ykdfmARIcQIq2QnTcIvbNUelhkECWR1z//+U/z+++/m3r16tk8G7NmzTKHHHKIt1dJ7xCrhnOZgAsOlctTRBEnwoOEDWUNs2okepbyxV0o0SGESAtUmlga6HFV1G/MSBbEBtlCGaFC3AbH+vTTTzfJswH+XiPDbhlJxrYEh8gFQQsE92dZSef8ICSCn0dIIDL8IFryOR5JoiNNyJQrihlncXDWhrAAuLJ47733bEXaqVMnm7KcvDjMBEuQKENcER9hIC6Y6RmxwXfnc2Us8ocwqwQE2wEEQtizwH0aLEdcBy0YfJ6lkJDoqABUsGQydD5k50cWJaDWGVVQ1jXx91ALCe4NKo9ElVKhwe8kERfPA+vk3cC1ERYUFwY5Nbp37257czNmzLBlRx55pHn33XfNo48+anbZZZdyny0qeokNkU24J8Pu8TCBgWgI1geI5aAFo1iQ6EgRGkoqOabCpgfmlkJTo5UBtY5f3d9YBB9G3kvW7JgvuN9DZUIlk2pvPx/BleJ6d8xvwm9OxrWxcuVKc/nll5uGDRuahx9+2JZx34wfP9688cYbNm6DZ82Je1kSRa5AXIS5PcLEcJiQcGn+RQkSHSnCzUfjwk3nX/IlcjhbBM2EwUaD61VoooOKBfHJb+P3l9dDLwRc7AbCG8ER/L8HWbdunbnllltsttDBgwfbbVwnzAi7aNEic/rpp9vriKUMd43rTRbDtRS5h3s42FlASAStGok6mWHtAM9Eec9FMSHRkSIIjGTNavmK62Hy6iwSNASsIx6cauc30wsF9qWHG3Yd3Od4de+znSh3A8fnGrvPAa+cB6/uWA6OGTw3B5/xHwfcsd3vcgT3ddfBv687N7c42JeFc+HVf55sFwrB68vzgNWivMBRRqCMHDnSBolec8019jhMyNajRw8rNq644gq7H0NfERvueLhrhg0bttH/T4hUCbt/uMeCzyb3Jc+sHwRDWL0WVn8Vq8skJbzMpCJJSC0br2hjcaVrX93SoUMHb4/ckc406KSJdunf473Y0jTvlLl1OPDAA721ks+41NK8+vfjvSBhZUBKX5ce2388/3dxvflfQP369e0r+/jTAZPu1+3Dd7Hu34fvcCmBeXXf5fZ165Tzu0ndTQptl1qY47j9gN/rjgGJfl++wu/3X99kIaXyXnvtVZq2nCUuVmMffviht0cJ/D/iIqN0H/99IESyhN0z/rrIwbPqf14dYfvy3BcLSoMeQfBdM7QvfnOWLoWocOnFOtx60KyYjlgWehaY013wKSZKridWBj/+72If13txlg5e/T0Ses3u/8L7rLtejNvfHZN93W90+zpYdy4TrDnsh5XDWT6KBX4/1ytZy01cVJiWLVtalwnZQyEuPuy1mzZtmp2szQ/HxqIUF2vW+sF6Ou4vUVwksqCGWSvCysLuuWTilERySHSkCA0QZjkaHv9SiDdlJir8sIecxoyGhsX5PmnYEHOJgrAocw0g157/ixMKbn9M82Gwn/u/0bBBon3Bfx343yNKnAiB8hrhsN+cD4Rdd36/+92JWLJkiR3G2qRJE/Pmm2/aMq4hM8CSb6NDhw62LAz+l1zf8r5DCHDPrx/uteC9y7MeVhYWg5FItIj0INFRAVxjd/fdd9uF9UKsJMMaHQgrp8zfOAcbYlcRuHL/Mbh2TgSw7uInnIXBHdf/GRomfwPl/27XyFN5+K0hfDdl/lgMt065q8Dcvo7g97qKyu1DWRjunILXIh/guvnzbiTD2rVrrSghboPhrlC1alXTp08f88UXX5j+/fvbsrCMpUKUR1jHLuzZ4vn0P+Pg6pcgErfZZ/N4JVGx1IFFDBUyjRQ3PBNQsd2oUaOc38A33nijufbaa72tiuMaGlJOA7/T38C6CbacWKCMhrl58+Z2nXJ3DCcITjzxRFsRsA/bjFZw1yt43Tg+x+M7ER516tSx65wP+yIKqIBY5/2lS5fa/Tku/wcW1jk3Psf7HJNyXjmXcePG2fecgGBf9vPv678O7new/wsvvGC/j3X2IVMm+3A8Frcvx6CcY7trFnX4XWeeeaa5/fbb7cgSfl95Pb9YLGafAa7Hs88+a9avX2/LTzrpJLvNDLBbbrmlPRaBx/fff7/9v3F9hAjCM0RdwT3ihzL3vDr8z6bDbfvLRPIwrxFD1oPuz7RREtohkoUgJRdI6Ccs+CjbpDOQNGoQ8FVogZlRg6DYeIVdGsjJ9SZ4tCziQsIG+LrPsDRu3Dj2xhtveHuU/O/iwmujfSoSkCoKE38wtiPs/ggr47NhnxcVR4GkEYNedljPD3UtMge9HHouzvog0guupaZNm9peJhBPw7VOdF/jLiHQFysOKcyBWV8feugh8/7779usohwLywaL+78RtxMXIaG+eFHYYEVz7k4/iZ5p9vcTtHIA1pCgRUREmyooD29dJAEVKQ9J0L/ojwnIFSdWq2ZeGDjQ2xIieTBT4zbaLi7szuzc2bq0wvjl11/NjPj9//bbb9vcG1Atft+1aNHCtPzLX0y1qlVtmePW224zv6xbZ497dFygqIEoDnA7cw8FXRzUnQhVP2FuE+fmlIsk+zz82GNm21tvNaeddppXkl4kOioAYTD07lwFykNDzzBMiWeTLbbYwvwabxSEqAiIZsR0oop+xIgR9t5fvny5V2LMeeedZzOM1q5d2yvZGNezDQsCFIWBi2Pyg0XYxV75YTto7aCMTpsEaTQ47rjjzPnnny/RETVQ7M7kj9iIwgMj0SGSxQXeJsMrr7xiR6B88sknXokxRxxxhBk+fLidO4Vjyb1YvCAi+P8HLRhh1l/2lQCNNpkWHYrpqCA8YDxQ9PwQHGG+SiGiCg2Ci99IBAm92rdvbyshJzjq1atnxowZY2bOnGmTfzGslllmRXFARyt439DpojxImKiV4BASHUmAVcNlx8Rk6ILj/EvYQydEVEEwJ7pnf/zxRzuL8n777Weee+45W4Z/neHYJPdCeBB0SgOClYPng+dCFBaIi6DAwKIRvG8QF8GgT1A2BhGGREcS8KAxVbuDCHxiOPyL/JEin6ChCI7C+u2338w999xjZ4DllW1wacyJ32jXrp0V2U5k8CyQslz3f36DpTYoMNhGUPrh/xzcDyQwRLJIdCQBosP5JnnoqKxxr/gXmQ1FVKFnGpzHJggWjcaNG1sLx4oVK2wZcwy98cYbZvz48WbXXXe1DZNrhHiPoa9sK54jv0jkCgmKCeq1MIER9v/WPSCSRaKjklDpMlmYEFEDk3e/fv2s4KChCVo2YNmyZaZNmzY2dsPFbTAPzYMPPmitGeTbcPB5LH6jR4+279EoiWgT5vagzgqWIzrCXGRhoiPsPhIiWSQ6KoD/4aTiZXKrRP5xIXIB9yhuEGehwzIRbCxIBU/cBvk5HOecc475/PPPTc+ePb2SDbjesKx60SSsDuL/HxQYYYGf1GP8f4MoQF6kG4mOJKESnzFjhl3I0eHW3RLWSxAiFzAJIYGe7p7EZcK6M4HTCDHTK3OsOFfKPvvsY2eEveGGG8zixYttmYguYRaIYPwF4A4O1k2J3CYSkyIbSHSkwMqVK20FjnnZH0Q6bNiwnCcGEwIQFNyfgJskmHKcnBtMtPbMM8/Y7a222spOvkfsxsSJE+0QWFwyItqEBW6GxWWElYECP0WukOhIEnoMzixJJU6vwi2USXSIKEAjg0kcSwaNjYu7+Pnnn02vXr1szg3iOODkk0+26aoZDrvXXnuVihNGo4TFAojckEhgBP9HYSNLKFPsjYgSEh0pgok6+BDjXgnrTQiRC2hoEMLOR//aa69Z6wbBocBIlClTplg3DDEcxHrQgGEZwXKHOd59VmSXsHokTABSBwXdKXR8gnUT/0eNLBFRQqIjDZCrQAFXIhfQSCUaTbBu3TrrDuT+/Prrr23ZgAEDSjONOosdsA9ig161BEd2CBMYYVaNsLiMMIEhRD4g0VEBEBi1atUyVapUKV1kjha5gF4sjVKw1ztnzhzTpEkTm+QL2I+ZZAcPHmzdKUADx6gWYpL4vHrEmSP4/4GwjkqY2wRxEVa/SByKfESiI0XonbAQVEplzXx5ysgocgmjDlyvd/369ebqq682hx9+uFm4cKEVxJdccomZP3++LfNDo0UPWnkXMo8/mNcRtF6AixvzE+bSFSJfkehIEQRH0ARKpaBeosgGDGkN6zXDRx99ZIfK3nrrreb333+39+Trr79uYze23HJLby+RSRASYQIjrFNCWZhVQ0NXRSEj0ZEiVOSYRRlWSAXBDJs0AsHeiRDphMaJzKIIXl798QDMkXLjjTdawYHwwLpx0UUXWesGQ2TLS4EuKgb/g6C1AiHh/984wsokLkQxItGRIogOzNL4wqlgiPjHJCr3isgUNGz+mYwZDuv8+aQub9asmbnuuuusa2W33Xaz1g2GxpJtFJHC5ySKK0/QKuE6IGEE9w3bz9UlQhQTEh0VAJHheimYUqlg5HMVmQArmn9WV4a00oDRWBEUylBYMuQCqctJbT5w4MCNrCGk6Zcorhxcy0QCI4hiZIRITJUYkZCiTKjwf/zxR28rnMmTJ4f6crPJFltsYX799VdvS+Q73He4TACLGo0egpcGsHPnzubtt9+27+2888520kGGyPpdKQyDxdIhQZwaXF+W4HWjoxEUHmyzH1YLIQoBrKTnn3++Oe2007yS9CLRkQTJVNplmVqzhURH4UFDh/jg3sJace+995rLL7/crFmzxr7fqVMnm/Rrhx12sBY3Z7JHbChmIDm4bn43B9tYK4LPM2VcV7lERCEj0REB8IfTwywLKqhcV/ISHYWHiw1AZHTp0qV05AqWD3JwkFHUDwJFsQLJg0WD5zvoEmE7aLlkX66rrq0oZDItOhTTkQTlCQ5Qr1JUFgSDExkOGrgnn3zS7LvvvqWCA7fJ+++/v4ngAKwhahTDQTQEhxsj0LjuQbBusr8fiTkhKo9ERwXAqkEF5IQGPaVgZSZEqnBP0cN2wuPbb7+1vQ4CRFetWmWqV69uh8YignfffXe7jwiHaxgcscP1DXOBIiSCYo9rzP5CiPQi0ZEi9H7c4kSHC+4TojLQ+DnRMWrUKGvdIM8GMCyW0SpDhw61OWI0BHYDXIugtYJrGdYRCLNUBF0rQojMIdGRIogLgsmEyAQEhJJwzlk3iNO59tprzf7772/TmbseebBnXiyEuUKwSISJsLBrJLeJELlFoiNF8Jn7TeBAjyqsMhQiEdw/5N/w97IfeOABKy5cD/2QQw6xFo/HHnvMDokFktLNmzevaGOIEAxBgZEojiXMPSK3iRA5htErIjUmT54c22677WLxio6RP7FWrVrFVq5c6b2beeINk7e2MdWqVfPWRJThXok3lPbeYRk3blwsLkBKt1luueUWuy/3mSsbNGiQLSsWRo8eHVu0aJG3VQLXrm/fvt7WBqZPn+6tCSEqw7HHHhubMGGCt5V+ZOmoAPSW6KmSEIxeJz3TbJhnv//+e3PEEUfY+TVEfoJFrEGDBqWWsV69epkLLrjAxBtNu411Y8GCBeaqq66y2wQ+OutGIbv1wuIvsGAErRo8Z4ncJkKI6CPRkSLOLI6Zl4qOijFbkHmyR48e3pbINxAa3Duu0SSxFy4Vt83IlNmzZ5t99tnHbgMCl89l8z7LBVyDMLdJWIB22AgUIUR+INGRIlSCzGUR9AuH9dTSzYoVK0z37t29rU2JxWLWCuJfRDSgUSWlOa81a9Y0LVq0MJMmTbLvETz66quv2jlTioGw+CcEfCJrhxAicwTbjJ9//tl7JzNIdKQIYuPLL7+0gX0zZswoXcIq0nRTq1Ytby0cRMfEiRNLFzc3h8g9uAVGjx5t6tata0XHzJkzbTnuFEQsI1WKBYRX0FrB9QlzUSrpnhCZ5Y8//tio3Vi2bJn3TmZQGvQUoTdGRRi0dFBhhg3bywRVqlSxAiOI0qBHm/Hjx9vhsGvXrrXbp5xyilm4cKGdJZb7Z9GiRaENb74T5h7CbZSt50UIkTxKgx4xqDzppSE+/AuVqBAOevPcFw5ybDAzrBMcZ555pnnqqadKp6UntXmhEjb7Ms9LWLyGEKKwkehIEXqiWBqCyAws/DjLFyOcDjjgADN8+HBbXq9ePZtd9IknnrDbTNzGPuxbCFaOsOyeYb8rzFoohCh8JDpSBFPxoEGDctpLU0bU/GC33XazI1Q++OADu922bVs7FJYRKtChQwd7H+WjlSxoyXFQHgTrYNi+QojiQ6IjReid0egHe2nZHMaH6BHRwzW433zzjXWXDBgwwG4TAExW0eeee8707t3bBo7mu3WD8w6758OGuWLVUB4NIQRIdKQIFSoTbpHgiZwLblFQXPGC2GA4LPfByJEjbSrz1157zb7Xpk0b8/HHH5uuXbvabaCxzifrBta9ZN0mim0SQpSFREcFoBfL8EcsDm6Rf7o4QXAgNmiYWYj6/vHHH611g2HVU6dONbVr1/b2zk/CrBcQlluD50DPghAiERoyWwFoaIK9PCrlXFe2GjKbXfyCww9DzggeJdlXvrlP+E2MNgnGDWGdQWRIUAhR2GjIbAShIUFk3H333XaJguAQ2SVMcHBfDBkyxM6RM3ToUOuGyzf4Dfw2Fj/EZeSbgBJCRA+JjgrgfPIEA7Kwruj84oIYB7/gYKTKiBEjzE033VRaznDYqBMWq0FZWG4NiQ4hRGWR6EgR1wukYUFosLh1UTz4LVuNGjUyPXv2tMGi3Bsu90ZYw51LwoKdw4az8ts02kQIkQkkOlIEgRHWO5R7pTggBOriiy82N9xwg90+7LDDbL6N6667zm4zDT2NeBRHcXDvBgNCOc8wMSLRIYTIBBIdKYK4CMtP4EzqonD57bffzFlnnWXdKEBMBwLjggsusNYNxAfbWA9yTZiQCHMD4jKJokASQhQmEh0pguigt9ixY0fb22UhR4N6hoUNsy/yfx43bpzdJtPoiy++aLbcckt7TyA6o5Tsi3s0KIQRQ2HiWPeuECJbSHRUAIYT9u3b16xcudKa28nZod5i4cJolHvuucd8+OGHdvvCCy+0k7VVq1bNbkMu3WsIjKDbhNEmYRa5qMWZCCGKC4mOCkLv0OUziII5XWSGmTNn2pwbb7zxht0mduO+++6z61Ei6E7B4qI4IyFE1JDoSAJ6jMwsi7jw9xTpXbId1qMU+Q3/U+ZJOfLII83SpUtt4rX69evbOI5cQkxG8H5DXARjNSAs4FkIIXKJREcSIDYYAok/3F+RU9mzjWtFwqNwIDD03HPPLbVo1KlTx1SvXt18+eWXNpYnmDgrU4R9Dxa2sLgM7sWgi0UIIaKGREcSYLouK2ZDSZMKh3bt2pkHHnjA2zLWuoGlY/Xq1aX5N7L1/0ZchInZMDGCxU3uFCFE1JHoSIJkKnP2CeuBivyAoOCGDRvaCdoAdxqCA+sGkH+D/282R3rwXWFDXwkSFUKIfESiIwmSERPso55mfoLloEGDBuaLL76w28Rv9O/fv1RwdOvWzcZMZPL/i2skLAYjLLeGhrgKIfIViY4koLEpK2aDBoOGQW6W/OOXX34xXbp0sdPRA3OofPrpp3biNsTGsGHD7P8+0/9bJ2iCrhOsGhIZQohCQaIjCeiB4jMnuHDGjBmlDQPrJAejUQhOBS6iz4oVK0zr1q1LXSrHHHOM+eqrr6xbBRAbmRoBEna/uPtMCCEKFYmOJMGSQSIwBEatWrWsz5/16dOnW7+7cnXkF7hOmDeFPBxw+eWXm1deecWuZwMsJ0G3HdYOJZkTQhQyEh1JQiNBz3fRokVWaDCKYd68eVaMSHDkF2QWJTD0888/t9u4Um6//Xa7ngnCrBeJMobqXhJCFDISHSlCbxQLBz1SNRD5x5w5c8xf/vIXG8OBtQpcttFMwX0SFBiIWFk1hBDFhkSHKBpef/1106pVKxuTg+DAXQYMl00XuEyCSboQqWFDXykXQohiQqJDFAXPP/+8Oe6448zPP/9sNttsMys4SPbF6JTgkNTKgAUjzJ1CkGhYUi8hhCgmJDpEwYMIaNu2rR0eC3/88YcVHIiNyo5OCQqJRENfsWpketitEEJEHYmONKF5L6LJwIEDTb9+/bwtY7bZZhs7JDYdAcAIi0RDX5NJKCeEEMWGREea8DdsIvdgzTj77LPNzTff7JUYM2rUKBvXgSBIRxAwlgssG0H3jAs2FkIIsTESHUlAA0IjxSsLjUpwm6G0IhqsW7fOtGnTxowZM8YrMWb06NGme/fu9v9WUTdHWOwHVo2wIFEhhBCbItGRBAxtpHdMo8NCjIB/G9eKMklGg++//94OiX3ppZe8EmMefvjhtEyShjslLLeG/vdCCJEcEh1J4A82RGSEmeY1MiH3fPbZZ+bwww83s2fP9kqMGTRokE1fnyr8P4P/U8QnVg39r4UQomJIdKQIgiPMnI4YEbkDodG8efNSN1f16tXNyJEjKzUnTthnnZVLCCFE6kh0pAjxAPR0O3bsaCd7Y2natKmN7RC54bXXXjMtWrSwE7g5GB5btWpVb6t8gtYLF/cRHJWkIFEhhKg4Eh0VgB4w056TyZIkUwQpKqV1bli4cKE56aSTzPr1672SEvifJBvHgeAI+//hVguL4RBCCFExqsQbzZJc0CJlaKyilPBpiy22ML/++qu3Vfj88MMPplmzZnbGWAd5OKZMmZKyNQK3iRuRJIQQxQqZm88//3xz2mmneSXpRZaOCkADhZndBZgS46Fhk9ll7dq15oQTTthIcNSsWdNMnTq1XOEQFn+jhF5CCJF5JDpSxDVM+Pqd+R7TfJQsHsXAqaeeaubOnWvXR4wYYd1dM2bMsMNlkyHMbZKOYbVCCCESI9GRIrhU/ENoHeolZwdiN9q3b28tGsCEbb1797YiImwocxhYQrB2JAoeFUIIkRkkOlKEhg3R4R/V8PTTT2vulSzAiJR27dqZ5557zitJbs6bsORdBANrmLMQQmQXiY4UoTeMO4Xe8tFHH22qVKlie9uVyQchyocYjhNPPNG8/PLLXomxM8Um4xJBmATFCTE5GnEkhBDZRaKjAiA4aMTmzZtnh83SY5ZpPnP89NNP5thjj93IMuGmpk/GpYIgDHOJCSGEyC4SHRXAxQLQ4LFO46eYjsywatUq07p1azNz5kyvpARGC4UJDlwpQbcJglCWKCGEyD0SHRXALzBchkrFdKQfrEitWrUy7777rldSArPFJhoWi0UjbGRKskGmQgghMoeSgyUJDZnLCYHAQGz4wdWS61wdhZQcjNliERbz58/3SkpAcIwaNcrbCv9fOMuTXCpCCJEaSg4WEQhYJBcEE4qh04JL2AgJUTFc0KhfcBDDMXny5I0EB+A2CQ59RaxIcAghRPSQpSNFaODoXUfRXF8Ilo4//vjDzqXi8nBAWUGj/C8QfBJ9QghReWTpiBgEJQYbP9wqweBFUTEuvPDCUsGx8847m+uuu866SrjmvAZjZ3CtsAStHUIIIaKHREclIO02S61atWyCMFE5hgwZYh588EG7vu+++5pPP/3UNGjQoDRmg9ewUSi4UjRkWQghoo9ERwU499xzbQPYt29fM2jQINOhQwdTv359711RESZOnGguu+wyu96wYUNrOQom/3JWJlmVhBAiP5HoSBFM/IgMzPw0iDSAMu1XjlmzZpmuXbvadVwq06ZNs69BVwpg1QgrF0IIEX0kOlIEgeHSZ9PzdoIjioGl+cDChQtNmzZtbADsZpttZrbffnsbTAoIOs0GK4QQhYNER4ogLuht0/AxNLNjx442nkOjJ1Lnhx9+MMccc0ypcENsLFiwoDT5GteYdbcthBAiv5HoSBGsG4gOFhfXwYRvbIvkYcZYLBxfffWVV1IC19M/ERtiTu4UIYQoDCQ6KgBiw7lTaCBxAyRKyy3C6dKli5k9e7a3VcKBBx4YOvOrZoMVQojCQKIjTci9kjw33XSTeeqpp7ytEhAcuFF0HYUQonCR6KgA/fr1s/kjqlSpUrpUdt4VrCU0uC+//LJXsinsE1zyjWeffdZce+213pYxW265pRUc7rfgplIMhxBCFCYSHSlCg0hOjuAcLJVxr9x55502IPWzzz4zxx9//EYpwP2QrfOGG24oXUhMlk+8//775vTTT7frXK/atWubt99+2woOl9yLco0EEkKIwkRzr6QIooMG0mXJdBDsGCxLhtWrV5tGjRqZb775xm6TkfOtt94yo0ePttsOZl1t3LixWbZsmVeyKVGee2Xp0qWmadOm9rVJkyb2NyKyGBIrl4oQQkQDzb0SMeiF40oJugDC8kkkw5w5c6yrxkGD/O6773pbG/joo4/MjjvuaKZMmWKtHOPGjfPeiT7MGnvCCSdYwVGzZk3rQtp6663ttWRYbGVdU0IIIfIDiY4KQF4Oeu3+mI6KxlcgOqpWreptGXPAAQeYL774wtvaANO88z3ffvutWb9+vTnzzDM3+U7yXFDulocffth7J7dwLrhWqlevbgXTrbfe6r1TIuI0OkUIIXLDBx98sFG7QQc3k8i9kiKuoQ/GcOAiqEiujvvuu88MHjzYxojA559/bpo3b27dKWVx1VVXmcWLF5sxY8Z4JSXulTVr1nhbJfgFTS7gPG+77Ta73q1bN3vdEBkuhkMIIUTu+O2337y1Ek488UTTq1cvuVeiQqK4jYr21nfffXcbD+JiNbAI1KtXz677ef75581LL73kbRlz6KGH2gnRgiAy/EsuYVisExwIKVxQ/NaKWoWEEEKkl2CbgUU9k0h0pAiig146Daeb2p6lojEd7du3N4cccoh55ZVX7Daig0ydwHe4BhqrBrOwYgFheeGFFzKmRNMBib86d+7sbRmzxx572Fempq9IwK0QQoj8R6IjRRABuAhoPJnW3i2VyS3BsXCzoDCZh8Qf80AMBBBN3KxZM9OiRQtr5SD4NOjiiQpff/21Ofroo0vNdptvvrk57LDD7DpoSKwQQhQniulIEdwDCIygOwXhwJJLojBklpgSRAXDYf0wp4qGxgohRLTRkNmIgWsgLH4jqlaHbIJ+Pemkk0oFh/MN1qpVK+eCTAghRO6RpSMJcHk88sgjtreOpYP1IIw+qWhcR7rItaWja9euZuzYsXYdweFurXnz5smlIoQQeYAsHREAoeEyhLI+ffr0jVKgS7cZM3HixFLBQeIvd02Id5HgEEIIAbJ0VACER3AEhgswzSW5snQw3JdJ23jdbLPNSocBt2rVqnT0jRBCiOgjS0cECRvyWcwxHWSxc3lGCBbFKjR58mSlNxdCCLEREh0VwN97p0fPdq7jOXIBvx1FjLsJiOm4+OKLrQBT1lEhhBBBJDoqCVYPGlmCTYsNcvaPHDnSrh988MGRmetFCCFENJHoSBIsGcyISu+dxFeMzvAvxSY6cKc4nx/Jv7baaquMTxQkhBAiv5HoSBIEB8KDOIWw0SvFloeCINFffvnFrvfo0cO8/vrrChoVQghRJhIdKYIrpZiHgCIszjvvPPPJJ5/Y7fr165v777/frldkll0hhBDFg0RHihA86awepEN3QZPFMlIDF4rLWcIQXVk3hBBCJItERwXAlYLwcK/FIjh++OEHO9Oto2XLlhqhIoQQImkkOlIES4dzrzClvcvPUQyNL1PVr1271gbObr/99mbatGmlv18IIYQoD4mOFGGI7N13322nnCeegW1GrlRmavuogwtl8ODB5tVXX7Xb7du3NytWrLDrmshNCCFEskh0pAgig5TfjFihMcbyUehTtr/55pvmyiuvtOtt27Y1U6ZMsevdunULnXFXCCGECEOiI0kQF7hTeMWlQA8f0cHC1O1Nmzb19iwsEFeTJk0yf/zxh83FgQABhFehiy0hhBDpRaIjCRAYDAd17hQHvXwCSWmACzW2Yfjw4Wbu3Ll2/cgjjzQ//vijXWf0joJIhRBCpIJER5LQyPoFhx8EB8myCgWsOcSozJo1y1x11VW27JRTTjEPPvigFVjDhg3TdPVCCCFSRqIjSVyvHvFBg4vQYN1RSJYOfiu/7fjjjzdr1qwx1atXN/fee68VXYgRJQETQghRESQ6UgR3CrEMLkdHIYLo+Pbbb83q1avt9umnn25q165t14UQQoiKItEhNmHmzJlm4sSJdh0B8sgjj9h1IYQQojJUiTE8QZQJVo2nn3661MXiZpR124DbYeXKld5WbiAt+a+//uptpQajcHAb8Zvq1atnLR1w++23m/nz51vrjv/3CiGEKDyOO+44c/7555fOIp5uJDqSIJkEWKRCz3WCsMqIDs6d31m3bl3zz3/+05adeuqp1uJBYCmCQ6JDCCEKG4mOCEBQZXnxG8nsk2kqIzqAuVUQHevXr7c5Ocg6ShCpEEKI4iDTokMxHUmQjJgohKBSRqggOODhhx+W4BBCCJFWJDqE5dNPPzU33XSTXd9mm23M0qVL7boQQgiRLiQ6ihiCR93IlO7du5vffvvNWjd++uknM2jQIBvLIYQQQqQLiY4ihoRmpHY/5JBDzBtvvGHLfvnlF/tKUGmiDKxCCCFERZDoKHIYJvvll1/a9apVq9pXUror66gQQoh0I9FR5LRs2dIsX77cbLbZZta9st12222U3l0IIYRIFxIdRYhLbtajRw/z0Ucf2XWmrgcEh9wqQgghMoFERxFCvEbfvn3N6NGj7fa2225rXn31VdOtWzc7Xb8QQgiRCSQ6ihBSmk+ePLnUujFlyhTTunVruVWEEEJkFImOImTSpElm8eLFdp3scwSOCiGEEJlGoqMI6d27t30lePTJJ5+060IIIUSmkegoEkgExvL666+XZhtt0qSJGTZsmF0XQgghMo1ER5FAIjBmku3UqZPd3m233cycOXNsQKkQQgiRDSQ6igiEBjPJwogRI8zmm2+u6eqFEEJkDYmOIoHZY/v372/XCRw9+eST7boQQgiRLSQ6ioThw4ebr776yq537drVvgohhBDZRKKjwCEnx8iRI82tt97qlRjTs2dP8+9//9vbEkIIIbKDREeBw8Rtzz33XGksB+BeUeZRIYQQ2Uaio8BheOwzzzzjbZVAGnQhhBAi20h0FDh///vfTSwW87aM6dChgx0+K4QQQmQbiY4C5rvvvjMvvfSSt1UCMR5CCCFELpDoKFCI5TjyyCNLrRxbb721GTRokKatF0IIkTMkOgqUq6++2nz++ed2naRgX3/9tRUiQgghRK6Q6ChQCBZ1Vo7Ro0fbzKPKPiqEECKXSHQUKPfdd5+58847Tbt27cwxxxzjlQohhBC5Q6KjQGFG2QYNGphnn33WKxFCCCFyi0RHgcKw2P/9738arSKEECIySHQUMOToUPCoEEKIqCDRIYQQQoisINEhhBBCiKwg0ZFH3HDDDaZx48Y278Ydd9zhlW7g999/99bygzlz5pjbbrvN28oPhgwZYt5++21vKz845ZRTvLX8YNmyZaZPnz7eVn4wbtw489RTT3lb+cEFF1xgVqxY4W3lB/l2L7/xxhvm7rvv9rbyg0WLFpkvv/zS20o/Eh15wvTp082MGTNszo1JkybZUSk02n78c6wI4fjll1+8NSHymz/++MNbE/mKREeewPT0TEl/6KGH2uXggw/Ou56VEEKI4qZKvHes7nEecOaZZ5r27dubLl262O1//etf5pVXXjFjxoyx27DZZpuZSy65xNsqoW7dut5a9CA1+2effWaOPvporyT6YG0i/8nuu+/ulUQf7hVGMuULq1evNq+++qr529/+5pVEn//85z9m8803N02aNPFKog8W0xNPPNFstdVWXkn0efTRR80555zjbUWf//73v7aea9mypVcSPZYsWbKRlZz6YuDAgWbAgAFeSXqR6MgT2rRpYy6++GLTtm1buz116lRzzz33mBdeeMFuAwJj3bp13pYxVatWNdtuu623FT1+++03+8p55gv5es75dL7EJlEt6b7ILJwzHRWWfCHf7uV8uC9+/fVX8/PPP3tbJdujRo0ynTt39krSi0RHnnDhhRfaHvbll19utwkk/fTTT+3NIYQQQuQDiunIE5o2bWpNuI733nvP1K5d29sSQgghoo8sHXkCvkEsHZdddpk1PePznjZtmmaOFUIIkTdIdOQRP/zwgw3+2nrrrW2Mx/bbb++9I4QQQkQfuVfyiB133NGcf/75dgRLmOBgZtnvv//e2xLphGsbZOnSpeaTTz7xtqIF8T5h5xxl5s2b561tDL8DwR01vvjiC7N48WJvKz9IdE9wL3/++efeVnQgML5Q6jR+C/f4mjVrvJLiRKKjAPjoo4+s64WMpTvvvLN58803vXeiC0P1qlSpUrpw7lHlwQcf3OT8evToYXbZZRebLyWK2TN79eplh/c6Pv74442uN0tURAnDvHfYYQcrpvfZZx+v1NhGkG2u/U477bRJMrxcQcZUIvuPOeYYc8ABB5hTTz3Ve8eYvn37bnSNozIcfObMmXbkG9eyWbNmZv78+d47xpx99tmmYcOG9rdE6TnkXMi+3Lp1640mrgy7l6MGIw3913LChAm2bib1AffE2rVrvXeiAaNsyP/krxMOO+ywja5xuu4NiY4CgNTcw4YNs1lL6X2NHDnSeye6LFiwwMyePdvGp7AMGjTIeydaMCyZxc/cuXPNE088Yc+boWZfffWVTYMdBajMunfvbmrWrOmVlEAjQ6PirjfLX//6V+/d3IG7cOzYsWb58uX2HE844YTSXDN33nmnueqqq+x9PXnyZHP77bfb8lxz1113mVWrVtl00StXrrRWJe4HeP/99ze6rzn3KEAdgSDifBDJt9xyiy0n7wU9b+5jFtJ2R0GMMtXA9ddfb60cH3zwgQ2cR/wD9wmi338vR4l///vfplGjRt5WCdzL3DPUe506dbK/LUoQK1i/fn1vy9hz5bpnoo6W6CgA/ImU6BE+8sgjNsFSlKlRo4Y55JBDbG8cS00UofLFfTJixAivpATK+vfv720Z25g/8MAD3lZuYSg1icuwwPihd3jggQfaSjwqFg7ATejPrHvEEUfYoGmYMmVKaVIzBNLEiRPN//73P7udSxBGfiHKOX/77bd2HdHh7usoXWeG1nPegEh2zJo1yxx++OHeVkmun+eff97byh2cE/esw2/NcPcy84NE6RoDnT6mqPDPg8W9QeI4x0EHHRQ6d1auePzxx+1IyPXr13slJdcYEcK9zDVOp5VRoiPPWbhw4UZ+5W222cbsv//+G1UsUeObb76xlQaZBbHKkK0vapUH7LHHHubee+/1tjZAJeJPqMRviQpXXnllaI+ESoTGnEyDV199tfnzn//svZNbEBPO4oK/+8Ybb7TmfqwH/vuaUVrc106Q5BLOd88997TrNOb0wHEXknmSCdTOOOMMa73BjE6vNwog7rimzZs3t6Z+LEjAObvfAjQ+7BcFsBZgQeL/7uLZAEvH/fffbzNnkjUTl0VU4P7FtUmCLQcZP/3JwaJUX7z22mv2fqDeCIoOOlO4ERFIuBLT1TmU6MhzXCa5n376yb46ojzJF72W/fbbz5p2SeN++umnm2uuucZ7NzokSnXOtQ4GNjKiKApUr17dW9uYnj17Wj8zFhn8+y4GKCpg4qdiO++888xpp51Wej/772tMvC7DYxTg+nFdiaGiYeTaI1LHjx9vhQgm9SjNooxY5nwQ+7feeqstowcenJ060T2UC4ibwq3G9XX361lnnWUbSsQ15n8aQ+feyiWc55FHHmljI/z1L1Zn3IcO6r8oZIrG6omrcOjQoXbbLzr4DVxz3MZkvyamJl2xaxIdeU69evXsK2oaqKR5CAlaiiqYcP29cXoqmZxKORP4A/G43lGe4wbondOYO9gOxn3kCnzHiDYqODffAwGEQNAmcF9zzaOSEI+eNo0MDUqLFi1sGa7Niy66yK5Dv379rA8/CmARdVYlshq/88479r7F4vXhhx96exnz3XffRaYnTlwH58ucUwQ1upgOtum0OJjuntiaXMNcWM7CxTrWWxdIzLV2Apr4FFdv55Lhw4fb60Z8DOeJoEfYcd4IDn8dzfvpqi8kOvIczI4nnXRSaeXMDU0kepRFx9NPP23N0Q4aG0zq+QIVIJWIAz9+FCqRsjj22GM3mgzwpZdesqb2XMN1xIxLXMfxxx/vlZY04NzXDOUErvHee+8dCdFBjA8WDXrZuDMdzIPEyBAHMShOkOQSrKHHHXectXAB7hMmWqxVq5Y9X66tg94vfvxcQ1xEhw4dvC1jRZITokcddZQVJA4sSn5BnSuw1tJQsziBxzrxKUyq564zr8FA01zAqCB3vizgXrmX/fUDQoTYpbQQE3nPlClTYg0aNIjFH7xYvPGLxW8Y753oEn8QYwcddFDs1FNPjcUfzli8R+i9Ez2mT59uz9HPmWeeGdtzzz1jTZs2jcUfRq80Olx//fV2ccR7s/Z8e/bsGdt1110J9/feyS2cI9c2uAD3dd26de19HRccsZdfftmW55p447fJ+bprHa+oY02aNImdccYZ9npPmDDBluea0aNHx+Idkdi1114b22OPPUrPd/ny5bG4MLLPIkvXrl1teRTgWjZu3DjWrVs3e79yD8OTTz4Z23777WMDBw605dOmTbPlUSL4/LHOuZ5yyimx/fffPzZv3jzvnejAfUxd56COpm6Li6lYvJNYev0rizKSFgiYyTDpRUHxJwtBgfjy/abSKOKCXOMPpX110GOkBxNvxL2S6JDonDGlb7fddqW9xlzjzjOIO29M0oymiNJ9Xd45E+9DECw5RqI2bXyi+4KcKLi46tSp45VEA64l9ywxEEELDCOEcANg7Y0aYdcZFziBxpxzFAk7ZwYkMAzfnz+nskh0CCGEECIrKKZDCCGEEFlBokMIIYQQWUGiQwghhBBZQaJDCCHyjETBrLmA1PT/+c9/vC0hykaiQ4gIQWpn5hshGc/1118fqcYlCOfKeVamweH38TuZOyiZFOdcm6ikFg+D35Dp8+O6kxberXPtctnocy785ijMiyOij0SHEBGCRpVGxDXGwaGNYeSqEeZcGfxWmcaG9MpOdCQD1yXKooPzQwhkCq41woZJw4D/AY1+rht8/of+6eeFSIREhxARw/VikyXK1pDycL+VxrO8SegQGzRsZLSNKpm2xNC48x1+ojJ5H/9LuVlEeUh0CBFh6MGSBMlV5v513rv77rttmb/cQRkNtOsF+49Fb5l1cJ932+49dzxeH3nkkU2Onyxhn3fn8uOPP9rXZFwr7IPowLoSbNjd+bNA8DfwfVwL//Vw+/DK4j8/tjlnd7wg7Ove41zcZ/3fGTy+W/fjyjmnZKw4HDuRyPAfyw/l/G7e88O2K3P/D7ftfh/lrLvzZptjcZ5BsYu1KpOCSxQGEh1CRByyzdLYMiNkq1atbGVPj5cGgAbYLQ7KccvUr1/f7k/PmDKYPn263aYhYZ4FjsVnmeeCqeUdffv2tZ9xDWq3bt3sOueQCkx6Bnye43DejrBzTwTn4qwiYY2b+w2LFi3ySjb8BhZ+M9fCXQ8H14NzolHluLyycN6cM9lbO3bs6O1dwrnnnmuPyfXFzcHCbwP3v3IMGzbMbrO/+27XgPMb+G7K2ceVJ4L3E1nB+D/yHUzW5lwvgKuH97g2/Bb/b+dc/e674DbXz91nrpxtjsW1Ct4L7BMUIkJsQvxhFUJECOY/CD6a/m3ejzdUm6w74g1dLC4ovK2SbRZg/3hjadf9sL//M5MnT7av/s/GG/RNvottjhkG5fEGytsqIbh/8HiJYO4Qvh/4PNcj3kjabUe8kSw9V3C/gbk7/OX8To4HHCt4DsyL4T9v3vfPleH/X4T9fv/x+C7/sfzf7f8s5xq8VkHY1/8/clDmL3fH5XoF/9dcI/f9UNZ9xnH8+3I85mdx/4ew+UN4X4iykKVDiDwglenG6UHTK6bXyYI53t/7DTPP0wPGnQB83vVs6YEzGym92vJ64kH4bv/3QkV7w3yGXjs9bdbptQetHZwr7ibw/wZ33nyOhd/vvwbBc2Sb7+E3cxx6+iwOLBxuG/dQIneHI3h8dz6Uu3Ve3flWhLDPut/qB0tJ8LqVhf/zrGP94bwbNGhg3SxB4oLEWxMiHIkOIfKARGZ1P27UBI0DCw0RC6bw8ho09kfYuAbJfR+uBOcy8B/D3wiXRXA/GtdkfosfjsF3IwTcgkgKNp78BgQBjS2f8X+P/3rwWf9vCZ4Px+X3snDt3Pvut/D9XGtEybBhw+yxKwLnwDE5Dt/B96WTROeV6PoH/1dB+N9xPdhv8uTJdnFuJUdQYAkRRKJDiDyAHnUY/obFNRo0qi4gEChPpnfL52644YaNGiUaV9cYcgzOg+MFG5swOB4CwOE+R3kq8L1+kQAcwx8U6nC/wd/4cf7+30/jWdb14DfTuDrcb3Wv/Ca+h+MGzysVOB6f5zjJXBN+k/96OoLXwOEsKf73uS/84gaR5ijvf8qxnLDl2Igv/7ErIihF8bF5/MbZENklhMgpNCpU7FTeVOg1atQw999/v1m6dKl9H5HB9rp16+xCo0Vj8fbbb5vmzZvb91n4/Lhx4+x7NAadO3e2x/N/NtgrbdSokXnhhRfMlVde6ZWUfB/nw/4ck1eOSSNJw71gwQJ7bnw35+qH/SnnmAgE9qXB45icy2233VbaKPLdwc8DVgB+B/udeOKJtoz9KWd/jsl07G5Kdn4T5+VvWDk2n+Hasj/riAqOyXF49V8P9ucYX375pf1t7Dtr1iz7Pt/De1xHrgsLv41z4xjuN7lrxW/n+/jNfDfn4LY5f86T38dxOBe+m/fCYH/28wsUjsd3cGzOz/1Gvptrz/+dc+V/xm9gm3IH58ln+J18Zvz48d47JSKEcnd9+V2UcXzK3XV0cBz3PxciEZraXgghkgRhgCjwN7aIEBrjVPpvNODOTeOgEXciMhHsT8Pu//6ogIDiN3F+QiRC7hUhhEgSBAeCwQ/bQatRedAwIzL8cJzy3DXOwhQ1OHd+kwSHKA9ZOoQQIgWciwSLBGKDhrYisR001BwLnAhJJraD72VJZt9sgYVDnnqRDBIdQgiRZyBYEsV+ZBvEkiwcIlkkOoQQQgiRFRTTIYQQQoisINEhhBBCiKwg0SGEEEKILGDM/wfh7L6QXUUNmgAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Isaacs et al. (2015) looked at the effect of **interval size** on the estimate of the correlation length, using data from ACE and comparing against the \"true\", multi-spacecraft value. The plots below line up quite well with the values calculated from our 6-hour intervals. In the accompanying discussion on pg10 of the paper, they state \"averaging intervals of 10-20 hours appear to have a special significance with regard to computation of correlation scales.\"\n",
    "\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "![image.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Taylor scale function\n",
    "\n",
    "Taylor microscale (time domain) = $\\tau_{TS}$ = radius of curvature of ACF at the origin. \n",
    "\n",
    "Can calculate using second derivative of the ACF at the origin, but this is not commonly done as it is very sensitive to behaviour at the origin. Here we use the parabolic fit method. This code is adapted from Kevin's `compute_taylor_time_scale()`.\n",
    "\n",
    "Previously this function took the number of seconds to fit the parabola over as the input, and then converted this to the number of lags. (This was chosen to be 2 seconds = 20 lags.) In line with Chuychai's method, this function now takes the number of lags `tau_fit` as input directly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'src.utils' from 'c:\\\\Users\\\\spann\\\\Documents\\\\Research\\\\Code repos\\\\reynolds_scales_project\\\\src\\\\utils.py'>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "importlib.reload(utils)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\spann\\Documents\\Research\\Code repos\\reynolds_scales_project\\src\\utils.py:773: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"-y\" (-> color='y'). The keyword argument will take precedence.\n",
      "  ax[0].plot(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "15.771723433957858"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LSxxKtc9q91Nr6fW5VrplDtUfu6CgAJIkxdU33Io4qYdBe5dSZ2cnVq5ciWPHjuH555/H2LFj8eSTT2Y4yuyl7XM91Lr8/PxI9bu3txf19fVwOBwx+2Nr+4rH03Cm7X9uOokU62b5yVT1W2vnzp3i7rvvFgsWLBB33323aG1tFadOnRI7duwQZWVlAoBYvXp1yt93xYoVYsWKFSnfrxCZqX6zn3D1O8P07lJqa2vDq6++CqfTiW+//RZ1dXWw2Wy4//77Mx0uyxGc1MOgPccGBlbJZ82ahV27dmHu3Lm46KKLkh5AIFPq6urwwQcfpGRfl1xyCVavXp2SfVmBcvqQjqGQOKlTTH3Z6+jRo3jhhRewaNEi3Hnnndi7d29K+oone98yM57f70d+fj6CwWDk3D4YDEYGWeSkzgLaKvnVV1+NI0eOYP78+ZgxYwbef//9YY877nTGfWvtsJi9ZDVzry6FMkySw+GAJEloampCdXV1ZLCFdBwD9/1OMe1NIW+//TbeeustzJw5E99++y1cLhd++OGHYb3H4cOHcfjw4RRFnL2S6SOeComMaFJdXR0pmdvb21FdXY3e3l7Y7XYEAoG09J7jkjrN1OfYR48exY4dOzB37lz89a9/Tbo76caNGwFY5zq13qihgUAADQ0NyM/PR3t7Ozo6Oga8JtaoomrKNW2lP3lZWVkksZSfROn1Tdd7H/VQx9rt0zVWOCd1mqnPsYuKijB79mxs2rQJJ06cwEMPPWTqSf0yqbe3N5KgSgKrzz9jjSqqTlRlNFCv14uamppBjVTRGq2CwSACAf1h55Vr1OrXaN9H6WLq8XjgdrsRCARQUVExYNKCocY3TxYndZppz7FPnjwJv9+P119/HUeOHBnWWNlWFK06OlRvsFg9x5TOIkoHlkAgEElkZZleUkcrxaM1cmnfx+VywW63o7m5OfI4EAjA5XJF+ranAyd1mund6XXDDTdg27Zt2LNnD957772cT2qn06nbM0vdQyzRUUW1/H4/qqqqAISrwTabDU6nE36/H3a7PaFGq9deey1q1Vn9PtovBOVLQrlx5U9/+lPM90pKIj1VjPwBYFf/Vv+YpUdZMpReaFVVVWLkyJHC4XCIH3/8MaF95EKPMvUNGunYd1NTk+jo6BAej0ccPnxYeDyeyM0fqaa++UP9Hk1NTYO2NW2PMiKqARAEYBNCtGjW2QDUIDxHlk0I0aJdhvAEeU1EFARgws61yVNXx8eNG4cXXngB999/P6644oq456MycrYHK1JXm5VSPV2NVko1XznPV2oG+fn56ZuDK5FvgHh+ANQDcMiPm3TWewC45MfNessQTmxHtPfI5pJa68YbbxQAxM033xzpP55JZimpc1UqSup0NLuWQTVJPBENNSaNjYi0LRE2AOMBOInIJZf6llVeXo6CggLs2rULo0ePxv79+2O+5uDBgzh48KAB0bFsZMS1FEnzvAGAQ072/CjLjgghvCI8JW6ldoehUAhOpzPyk+hAcmYyZcoUTJ06FSdOnMCOHTswceJEtLa2Yv369WhtbdWdOGDLli3YsmVL2mIKFw7MaKn63GOeUxPRdQDKAZyFcILuE0K8PsRL9iFc2gIAhBAD2u2FEBIReeXfQWW9ehkAFxG9JsLzVg9SVFSEVEy7YwbKOfZpp52Gbdu24V//+hdCoVBKpodNRl5eHg4dOoSCgoK0j7XGBjpx4gRGjRo17P1ETWoimgDAhXASL1IvJ6J5ALqEEK06L/UCqJL/IXyq19UIIbxyddtFRL0Il9DQWRYEYCeifITPsS1LueQ1bdo03HDDDdiwYQMqKytTMj1sMi644AJ8/fXXCIVChr0n+8l555037H0MWVILIQZdSBNCfA7gT0R0VpTXSAgnNhBuzVaWe+XfQdV6RFumfm0uGDFiBDZt2oRJkybhrbfeQlVVFY4ePZr09LDJGjVqFCZMmGDoe7LUinpOLScvAICI7tBZ/126gspV559/Pv785z+jt7cXn3/+OebMmYOrr7465jk2Y2rxXqcuAzDUeTRLkcrKSsyePRubN2/Gc889h7fffnvA4IZEhJtuuinTYTITi7f1u5SI5hLRHURkjpnXLWzVqlU455xzMGfOHHz88ccD5vPav38/SkpKeA5pFlW8SR0QQrwC4H0AVWmMhyHcr3nDhg348MMP8eGHHw6Yz2vy5Mn46quv8NVXX2U6TGZS8Va/txLRmfJ59ivpDIiF3X777aisrMSWLVvg9Xrx/fffR0ZSefjhh/Hf//4XDz/8MN+6yQaJK6mFEO+nOxA22Nq1ayNTvrzzzjsYMWIEWltbsW/fPuTl5WHjxo186yYbJOpXPBHdSUTjh1g/qEWcpda5556L1atX491338WGDRsAhEdSycvLw9ixYyPn2IypRS2phRDbiOg6IpqPn3qTnQ3gMMIdT7gaboB7770Xf//737Fo0SLccsstKCkpwYkTJwBgwJzZnZ2dcd/lxawtVueTnQB2AgARncXXpo1HRHj55ZcxefJk1NXVYdu2bbjssstw8OBBzJkzZ8Cc2ZnoVsrMZ6jq93VEtF2pggshviOiM4lohmHRMQDAuHHjsGTJErzxxhvYvn07nnjiCbzwwguYPn06Dhw4MOiSF8ttFO3OELl/tx9ABcJ9uOcjXPW2CSEeMixCHU6nU1jlho549fX14eKLL8aPP/6Ijz/+GHl5eQAGzrwpSRIeeOABEBFXxy2EiDqEEHEP9j5U9btLCPE5EXkBLEZ4IAMHcqxPtlmMHj0aa9euxfXXX48nn3wSCxYsQHFx8aCBDbk6zob6Cq8kokvk8+j/E0J8LoTYpu4TzoxVXl6OiooKrF27NjL2t3byAK6Os6GS+jsAvyOiHQA8RNRARDOIaK5BsTEdL774IogI//jHP3TXl5SUDOqBxnLLUJe0FqmfE9GlCN9f7QT3KsuYCy+8EOXl5XjzzTfx5ptvDrq5Q28uL77klVviHk1U7lX2vjx4Asuga665Bvv27UNdXR1cLhdGjx4dWacdZ1zdkMbn2Lkh4a9sPqfOvJ/97Ge49dZb8dlnn+Hll18eclv1XF58jp0beIaOLFRVVQUhBLq7u/Hss8/i3nvvxdlnn627rXouL+Ucu7+/H21tbVwltyhO6ix04YUXAgBWrFiBSy+9FMuXL8fKlSt1t9WeY0+bNg1tbW1cJbcw/nrOQp2dnejs7MSUKVPwwAMPYO3atejq6tLdVnvJa8SIEVwltzhO6iyktHwDwLJlyzBq1CgsWrQoxqt+wpe9rI2r31nu/PPPR319PZYuXYo9e/bgqquuivkavuxlbZzUFvDEE0/A6/Xi8ccfj5wjD4Uve1kbfx1bwNixY7F8+XK89957aGlpif0CDT7HthZOaou47777UFJSgqeffho//vhjQq/VnmMrAy/wWOPZiavfWeiee+4ZtGzkyJFYvnw57rzzTmzZsgWzZ8+Oe398p5e1RL2f2sxy8X7qeAghUFZWhp6eHhw4cAA///nPk9rP+vXr0dnZicLCQvT09KCkpAQLFixIcbQsXoneT52W6jcR1chzS1forLMRUb16fZRlUfeR6z766CN89NFHg5YTEZ5//nl0d3fjlVeSv+eGq+PZLeXVbyKqB+AXQgSIqAmAtuVmMQCfEMJPRM3y+gHL5Fkwh9pHTvP5wpOJXnzxxYPWlZeXY9q0aVi2bBlmz56NsWPHJrx/ro5nt3SU1GVQTTQvTyQfjU1O4AHLAExPYB9MhYjw3HPP4eDBg1i3bl1S++CBF7KbEa3fkuZ5AwCHnKj5QyyLuo9QKASn0xn58Xq1s+Dmtquuugo33XQTPB4PJEka9v64Op5d0tH6vQ/h0hZAZO5pqJ5LROSVfweV9eplsfZRVFQEbigb2vLly+FwOLBy5UosW7ZsWPvi6nh2SUdJ7QXglEtdn7KQiGrk33YAVXIDWEOUZbr7YPG79NJLUVFRgZdeegmHDx8e1r64Op5d+JJWFlKSNNo91IoPP/wQl1xyCZYuXYpnnnkmZe/PwxIbK5VDBDOTipXMiilTpuD222/H6tWrUVdXh7POOisl78/VcXPjr9Ms1N7eHnebwpIlSyBJUtIt4Xq4Om5unNRZaPfu3di9e3dc2zocDsyaNQsvvvgijh49mpZ4uHXcXLj6nQOWLFmCyy+/HH/84x9RX1+f8v1zddxccqqk9vv9aGxsHHIbSZJQWVlpUETGmDp1KmbOnIkVK1bg2LFjKd8/V8fNJaeS2uPxxCypbDYbqqur4Xa7DYrKGE8//TRCoZAhHXW4Op5ZOVP9bmxsjLsErqioQENDQ5ojMtaVV16JGTNmoLGxEfPnz8dpp52Wtvfi6nhm5UxSb926FTt37hywrLy8HADQ29uLnTt3wmazRdY5nU74/X64XK6UxbBlyxYcO3YMPT09KCwsRFFREe64446E91NbW5vU+y9ZsgTTp0/Hq6++ivnz5ye1j3hoh0tav359pDoOAPv37+ekTqOc6Xxy9tlnR+1Z5fV60dHRgaampgHLJElKWcOS0jHj+PHj6O7uRklJSUr2mwghBC6//HIcOnQIBw4cwMiRIw15X+6sMjzc+SSK/PzB94kEg0H4/f7IrYza7aONpZ0MJYk//fRTTJo0KbJ8+/btKCkpQWdnJ2bOnBnXvt59910A4Sp1IogI9fX1qKiowOuvv25YgyBXx42Vs1+PgUAAlZWVcDqdSVdnk/HFF19gzJgxAIDjx48DAC666CJcffXVAICenh688847Q+5j7969kal0EnX77bfjV7/6FTweD4yqpXHruLFyJql7e3sHPG9vb0d1dTUcDgeCweCg7YPBIAoKClIeRygUijzu7u5GKBRCZ2cnNm/eDAD48ssv0d3djZ6enpS/NxAey+yJJ55AR0cHdu3alZb3iIVbx9MrZ6rfdrsdkiRFGsOqqqpQWloKn88Hm802qHre1dWV8urp8ePHUVRUFHk+btw4fPnllygpKUFHRwcAYNKkSQiFQpFGpXS477778PTTT6OxsREzZsxI2/tEw9Xx9MqZkrq6uhqvvfZa5LnNZkNXVxd8Ph+am5sHNJIB4ZI8lS3fADBmzJi4W7vTVVIDQF5eHh599FFs374dH3zwQdreJxqujqdXziR1TU3NoMSNJtWXsqL59NNPEQqFcPz4cfT09OD48eMYM2YMjh07FjnfTpeHHnoIZ5xxRswedkbg6nhq5cwlLSCcrIFAYMjLVJIkwe12x/0FkAl9fX0AgNGjRw9rP3/4wx+watUqfPbZZ5gwYUIqQktKf38/du/ePaA6vmnTpsglsDlz5uR0dTzRS1o5ldRsoG+++QYTJkzA/PnzsWbNmkyHE8Hjjg9kinG/WXq1tbWhra1t2Pv55S9/id/97nfYuHFjSgYoTBW9qXb7+/u5Sh6nnGn9thKlpfzaa68d9r7q6uqwefNmbNy4EY899tiw95cK2tbxadOmoa2tjWfmjBOX1DnO4XDgmmuuwZo1axKeWC9dtK3jI0aM4Jk5E8BJzVBXV4fu7m7885//zHQoUXELefy4+s1w6623Yvz48Vi9enVSd40ZgTusxI9LaoaRI0di4cKFeOeddyLn62bDHVbil5WXtIgoBKA703GwjDoDQCGAUwBGAlC64OUBOAEgPaMsZsY4IURR7M3CsjKpGWPRcfWbMYvhpGbMYjipGbMYTmrGLIaTmjGLMTSpichFRJ4h1tfI21QYGRdjVmJoUgsh/ADseuuIqB5Au7xNuZFxMWYlZuomWgagRXlCRA4hRED1vAZADQCMHTu2VD3MLmNW1tHR0ZNI5xMzJbWWpH4ihPAC8AI8SALLLUSUUO9JMzWU7QNgU54IIQaP28sYi8nwhjIAdiJyqJbVyA+9AJzyusFTZjDG4mJo9VtuBCvVLPPKvyXI1WsAATDGkmKm6jdjLAU4qRmzGE5qxiyGk5oxi+GkZsxiOKkZsxhOasYshpOaMYvhpGbMYjipGbMYTmrGLIaTmjGL4aRmzGIMvUtLvs0yCMAmhGjRWe8C0AvArreeMRabYSV1rDHI5IS2yUMY6Y5jxhiLzcjqdxlUQxSpB0oAIvdaLyaiZgB+A+NizFIyeU4tqZ8QkR2AG+FRTwYNIywPH9xORO2hUMiYCBnLQkaeU8cag6xCCNEIAEQEIrKrt9EOPJj+cBnLTkaW1LpjkKnGKGshogp5fS8PPMhYcgwrqaONQaYaoyyIcMv4gPWMscTwdWrGLIaTmjGL4aRmzGI4qRmzGE5qxiyGk5oxi+GkZsxiOKkZsxhOasYshpOaMYvhpGbMYjipGbMYTmrGLIaTmjGLMdvAgxUIj4jiUAZMYIwlxmwDD+bL63kkUcaSZJqBByEnupzcLu2LeYwyxuJjmoEHER6/LKiU5ERkU68UQniFEE4hhLOoqMiYCBnLQkYmdayBBzsMjIUxyzLNwIPyWGUOufrtk8c0Y4wlyDQDD8qPucWbsWHi69SMWQwnNWMWw0nNmMVwUjNmMZzUjFkMJzVjFsNJzZjFcFIzZjGc1IxZDCc1YxbDSc2YxXBSM2YxnNSMWYyhSS2PXuKSxyKLto1jqPWMsaGZZowyFReAfGOiYsx6zDRGmTI+md/AmBizHNOMUUZEDrkU18UDDzIWHzONUaYeSbSUBx5kLDlmGqMsIJfUBQbGxJjlmGqMMvm526iYGLMivk7NmMVwUjNmMZzUjFkMJzVjFsNJzZjFcFIzZjGc1IxZDCc1YxbDSc2YxXBSM2YxnNSMWQwnNWMWw0nNmMVwUjNmMYbdeglE7p0OArAJIVo062wA7MqPEKLRyNgYswozDTxYBUCSk71aO/IJYyw+phl4UB6uKKh6LqnX8xhljMXHNAMPKuQSvVK7nMcoYyw+Zhx4sEW7nDEWPyMbyrwAqogI0Aw8KITwygntAdCL8GD+pQbGxphlmGbgQbkBjROZsWHi69SMWQwnNWMWw0nNmMVwUjNmMZzUjFkMJzVjFsNJzZjFcFIzZjGc1IxZDCc1YxbDSc2YxXBSM2YxnNSMWYxpxiiLZz1jLDbTjFEWxxhmjLE4mGaMsjjWM8biYGj1W0NKZL1cNa+Rn/5ARB+nIabhKATQk+kgdHBc8TNjTAAwMZGNjUzqWGOUDbleHiHFCwBE1C6EcKYr0GSYMSaA40qEGWMCwnElsr2R1W8vAKdcrR4wRtlQ6xljiTHTGGW66xljicnW69Te2JsYzowxARxXIswYE5BgXCSESFcgjLEMyNaSmjEWRSYvacXFjL3QzDp7ZzyfhdwQaTeyx14cf8MKhC9hOoz6vOKIyYXwxBJGf1YuAOVCCHeU9TH/xqYuqc3YC82ss3cm8Fm4EJ4BxRBx/A1dAPLl9UZ9KccTk00IEUD4y9kwcky67xnv39jUSQ1z9kIb1uydmYpLXuYC4DcoHkWsuMrl5S6Ev3AyHpOcNIuJqBnGf15Diev/3exJrSUNc3066L5ntNk7DSSpnxCRQ/5nzTRJ89wGIKiUPhmal1xSPyEiOwA3wv0lPBmIJ16S3kKzn1MPqxdahmLK1Oyd8cblAFBMRDaDahGx4uowIAatWDFVKOf2RAQishv0vxVLXP/vZi+pzdgLbciYVLN3NgFoNiimmHEJIQJyaVhgYEzxxOUF4JA/N59BXzSx/q9aiKhCXt9rZELLn4NdXbVO9P+dr1MzZjFmL6kZYwnipGbMYjipGbMYTmrGLIaTmjGL4aRmzGI4qRmzGE5qxizm/wML//o7UJx90gAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 237.6x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambda_t, fig, ax = utils.compute_taylor_scale(\n",
    "    time_lags_hr, r_vec_hr, tau_fit=15, plot=True, show_intercept=False\n",
    ")\n",
    "lambda_t\n",
    "# Set show_intercept = True if you want piece of mind that the value returned is actually the x-intercept\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Chuychai (Richardson) extrapolation method\n",
    "\n",
    "We can't just use the above function for some very small lag close to the origin, because as noted by Chuychai et al., \"it is not practical to compute this limit because the data has a finite time resolution and there may be limited data available at the shortest time lags\". Therefore, we can calculate the Taylor scale from a parabolic fit for a *range* of values of $\\tau_{fit}$, up to $\\tau_{max}$. Plot these values as a function of $\\tau_{fit}$, then draw a straight line through the points back to $\\tau_{fit}=0$. \n",
    "\n",
    "See lit review spreadsheet for ranges of $\\tau_{fit}$ in other studies.\n",
    "\n",
    "Chuychai's notation:\n",
    "- $\\tau_{fit}$: parabola is fitted from $\\tau=0$ to $\\tau=\\tau_{fit}$\n",
    "- $\\tau_{TS}^{est}(\\tau_{fit})$ = estimate of $\\tau_{TS}$ for a given value of $\\tau_{fit}$\n",
    "- $\\tau_{TS}^{extra}$: estimate obtained by the extrapolation method\n",
    "- $\\tau_{TS}$: final estimate after applying correction factor\n",
    "- $q$ = dissipation scale index\n",
    "- $\\tau_{d}$ = Kolmogorov scale (time domain) - point where the inertial range terminates and the spectrum steepens\n",
    "\n",
    "<u>How do we choose the upper value, $\\tau_{max}$?</u> This is investigated in Fig. 5 of Chuychai. Weygand et al. (2007) show an example of reaching a stable estimate as $\\tau_{max}$ increases, but Chuychai shows that this is dependent on the spectral index. In particular, they note that we are more likely to reach a stable estimate of $\\lambda_{TS}$ after extrapolation when we have a steep spectral index $q$ in the dissipation range. A smaller $q$ means we do not obtain a stable estimate.\n",
    "\n",
    "**Here we have decided to set $\\tau_{min}$ = 10 lags $\\approx 1s $ and $\\tau_{max}$= 50 lags $\\approx 5s$.** This is roughly in line with what Chuychai & Matthaeus did for ACE data, while reducing $\\tau_{max}$ due to understanding that we will not get convergence with increasing $\\tau_{max}$ due to the relatively shallow values of $q$. This also matches their recommendation that a good estimate is obtained by an extrapolation of the curves evaluated near $\\tau_{max}=\\tau_d=4s$.\n",
    "\n",
    "Chuychai et al. then developed an additional correction factor \"which can be used when estimates of the [slope of the] high-frequency spectrum of the signal are available in some way, whether it be observations, theory, or an informed guess\". The equation for this final estimate is given in Eq. 10 of the paper, and is coded into the following function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compare the following to Fig. 4 in Chuychai, and less directly to Figs. 5 and 7 in Weygand et al. (2007)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.620638938079269"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Not applying Chuychai correction factor\n",
    "ts_est_extra, ts_est_extra_std = utils.compute_taylor_chuychai(\n",
    "    time_lags_hr, r_vec_hr, tau_min=params.tau_min, tau_max=params.tau_max\n",
    ")\n",
    "ts_est_extra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.894755492195783 0.04590859183297959\n"
     ]
    }
   ],
   "source": [
    "# Applying Chuychai correction factor\n",
    "ts_est, ts_est_std, fig, ax = utils.compute_taylor_chuychai(\n",
    "    time_lags_hr,\n",
    "    r_vec_hr,\n",
    "    tau_min=params.tau_min,\n",
    "    tau_max=params.tau_max,\n",
    "    q=df_wind.loc[timestamp, \"qk\"],\n",
    "    fig=fig,\n",
    "    ax=ax,\n",
    ")\n",
    "print(ts_est, ts_est_std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GBubMmUNGRgZPPvkkra2tLFu2LKprkO12OxC79dTxQIup1txvs9mMy+XCbrfjdrspLy+nra2N6upqvdz3PYDa2lqampr0sE+3280999wDQEFBgZ+INTd83rx5lJSUYDAYuhwDUFVVpcd3NzU1UV5ejt1u12O/e3ubEEmUqHtJsGgpbQGDwWAgKyuLefPm8dJLLyGlZNmyZQkTgZaMBLuPDoy5Likp0QULdHmvqKiIiooKfaGFFpEWGI/tiybMUK5+WVkZTU1NlJWV6b2zb/x5PFGi7iXBFokELmCYOnUqRqMRm83G6dOneemll5SwI0iwmGstLLO7eOzs7GzcbndYseHJjBJ1BAh0yfPy8sjLy2PHjh3Y7XY6Ozux2+1K2BEiMOa6u/eysrJ097utrY2KigrMZnOP8diBseLh3GcHxp/Hi7SP/Y4EoeLHR4wYwcaNG/n000+5++67qaqqiug9tor9Th9U7HeM6S5+/LrrrmPChAm88sorjBo1ikWLFkWs3b6uflKkNkrUUcDXHf/yyy+pqKggJyeHZ555hnHjxvHggw9GpJ14bZj40EMPsXPnzojUdfnll7N06dKI1KXwoEQdBYJFoXV2drJ161YeeughRo8ezW233dbvdo4dOwbAyJEj+12XIjHQxgSsVmuf61CijgLBotB+85vfcNVVV3H48GF+8pOfMGbMmH79cAArV64EYj9PrXrW/uNwOMjKysLlcukDdi6XS985tT//G2o4NgZoU17jxo3jpptuYsyYMdxyyy3s2LEj3qalJMkwRVVbW4vBYMBsNpOVlYXdbicrK0sfje/PZ1CijgG+a7S/+eYbnnvuOYYOHUphYSE1NTX92kJX0ZV4hWr2Zpui0tJSvWduaGigtLSUtrY2TCYTTqezXyGxyv2OAcEyiVgsFmpra7nvvvsYPnw43//+9+NtZsLhu7iiqKiI2tpanE4nixYtIisri4aGBhobG/3O8d2md8GCBSHDQeFMoIq2SKSgoEAXlvboLcEWnARrp7i4WH8/8Pj+7heueuoYEJhk4LPPPsNkMnHzzTfT0tLCwoULY7IAJBVoa2ujoKAAu92O1Wrt0jsuWLAAq9WKzWbTg0Cqq6v12G9ftHDTkpISPSTUZDJhtVr1e9xgva/L5aKmpqbLQ4spDzwnsJ22tjZ9729tD3OXy4XT6dTr6g8J21MLIUzePFumULm0khVtymvs2LFccsklbNmyhWXLlvHAAw/0qp5o7BmdqIRyR7u79+wpHFSLANOi0pxOpz76rJUFG7QK1YuHGuQKbEe7aFRXV+vPnU4nVqtVX7DSH6KVSytkwnghhAEoA5ycSTDvV4Ynl5ZdCOEC4hsdHwV83fFbbrmFF198kYcffphvv/2WIUOGkJeXF1Zu7csuuyxGFseH/Pz8oOGWvmGfvd0qOBCHw8G8efMAjxtsMBjIz8/H4XBgMpn0XWXDWSO9du3akK6zbzuBFwTtIqGtRluxYkWPbXWLlDKiD6ACMHuf24O8bwOs3ufVwcrwCNscqg2LxSJTifb2dpmTkyMHDx4sb7/9dvmjH/1I1tfX93jeF198Ib/44osYWCjlrl27YtJOT9TW1kqbzRa1uu12u2xsbJQ2m00eO3ZM2mw22dTUFJX2ysrK9Oe+bdjt9i7HBvv+gQYZRB/RuKcuwCeftDepfCgMQohAP8YA5AD5Qgirt9dPaYYPH85PfvITANavX8/w4cPZtWtXj+e9+eabvPnmm9E2L22wWq2UlZVhNpupqKjAYDBQUVERlW2KNDdfc7UdDoc+MNjf+IVY3FO7A14vAsqEEG1AVoiydunNkimEqMWT6lanpaXFL0SyrKwsYXMFh8uMGTOoq6tj8+bNbNy4keLiYr+90MJxx9MBq9Xa73/6RMBkMunrv4GI/v/2KGohxGygCBiBR6DbpZS/6+aULknlfd+UUrqFEFXevy7tfd8ywCqEWCuldAdrYPTo0STSKq1IMHPmTJ588kmeeOIJNm3axNatW/WglS1btiCE6HOSuUghpYzqTi6K4MhezoyEvPQLIYxCiHuAo1LKx6SU/yKlXADsEELcI4QoDHFqFR7X2YxPwnjNjfa62/OEEMV4euhgZWvxJK234rnHTnm0aa/33nuPadOmsWjRIgYOHOi3F1o8yczM5OjRo2rqLcZIKTl69CiZmZlhn9NtTy2l7DIMJ6VsBlYIIUaEOMfNGXc5WNJ5FwHudLAy33PTiczMTNauXcvll1/OunXrKC4upr29vc+ZIyPFhAkTOHjwIC0tLXG1Ix3JzMxkwoQJYR8fUtRe8QIghJgb6HJLKb/sk4WKHrnggguoqqri9ttvp6mpiccee6zLfuMzZ86MaS6vQYMGYTQaY9aeou+EO1BWAHR3H62IMD/+8Y/11V1PPPEE77//vt9+44lwj61ITMIdTrUIIe4WQswVQpwTVYsUOkuXLmXixInccccd7Ny5s8t+4wcOHODAgQPxNlORYIQraqeU8hVgBzAvivYofDjnnHP4zW9+g8vlYuPGjX7ZOKdOncrTTz/Ngw8+SH19vVrppdAJV9RrhBDnSCmbveJWxIjrrruOhx9+mHfeeYfLLruMvLw85s+fj5SS7du3c+TIEVauXMnGjRvjbaoiQQhL1FLKHVLK9mgbowjO008/TV5eHi+++CK33XabvtIrMzOTYcOGJcSUlyJx6G6e+lYhRE4378+NikWKLmRmZrJq1SqOHDmir+TKy8vjxIkTHD9+XE//o1BA91NabwshZgsh7uVMNNlI4BjQpNzw2GKxWPi3f/s3nnjiCYqLi7npppu48sorOXLkCPPnzw865aXCStOTsDfzF0KMSJS56UTbzD9WfPfddxQUFNDS0sKuXbtobW0FIDc31y/FrtvtZv78+WrKK8UJtZl/d+73bCHEu5oLLqX8UghxTjfhoYooM2jQIFasWMEXX3zBggULyM3NJTc3FwieYleRnnQXfGIC7gVKvCul7sXjehuA+uibpghGQUEB//qv/8rSpUuZOXMmFouF3NzckCl2N2zYoFzyNCOk+y2EKJRS1ntjvBcAdsCMZ866OehJMSJd3W+Nr7/+mosvvphvv/2Whx9+mMrKyi75vAJT7CqXPPXotfuNp4e+3Hsf/VvvHPXb8Ra0As4++2xefvlljhw5Qn29x2kK3NwwIyNDueRpSnfu95fAD4UQiwEphHDiWUppUiPf8eeGG25g2rRp1NXVsWfPHqZOndrlmECXfOrUqWqEPA3obkrrMd/XQogrACuQDyhRJwA333wzn332GeXl5WzYsKHLBgbB9ht/7bXX1KKQFCfsy7Q3qmwJ8FiPBytiwvDhw7nxxht5//33eeutt7q8H2y/ceWOpz699r3UPXXiMG/ePJYsWYLFYuHRRx/lq6++6vZ43/Q/vu748uXL1aKQFCJhN/NX9MzEiRMBWLZsGVdffTVPPfVU0H2yNZQ7nh6oUZIkZvfu3ezevZurrrqKf/7nf+b555/ns88+C3m8csfTAyXqJGbdunWsW7cOgGeeeYYhQ4bw4IMPhr05YKA7rhaFpAbK/U4Rxo4dy8KFC/W11z/4wQ96PCfQHVeLQlIDJeoU4v777+eVV17h4Ycf5vrrr2fIkCHdHq+549p9tO+iEHWPnbyoy3AKMWjQIP7zP/+T5uZmnnvuuV6fryLQUgMl6hRj1qxZ3HLLLTzzzDMcOXKkV+cGu8c+ffq0mvZKMpT7ncT8+Mc/Dlr+zDPP8Mc//pGFCxfy0ksvhV1f4D124KIQ5ZInB6qnTmLGjh3L2LFju5RfcMEF3HvvvVRVVbFnz56w61OLQlIDJeok5uOPP+bjjz8O+t6///u/M2zYMCorK/vVhopCSz6i4n57k+G5AIOUsibgPQNQhidXlkFKWROiLGQdCg9aKtTLLrusy3ujR49mwYIFLFiwgA0bNjBz5sw+taGi0JKPiPfUQogKPBnuHXhS4AayAM9GCw6gNFhZGHUowuDBBx9k4sSJPPLII33uUVUUWvIRDfe7AJ9E896UtqEweNPY+pUBs7qrQ0s6rz2qqgITZioAhgwZwi9/+UsaGxv57W9/G5E6lTue+MRi9Nsd8HoRUCaEaAOyQpT9vbs6UjHpfLS47bbbeP7551mwYAFz587tVZ7jYCh3PPGJRk+9HU9vC+i5p/F57QaqpJROwCWldAWWAeu7q0MRPhkZGSxevJj9+/dHxKNR7njiE/a+32FX6Bn0mgc04Nn6qMZbXialrPK621agDY+onYFl3keXOjTSfeNBjWPHjgEwcuTIHo8tLCzk008/xeVyMWzYsIjZELjf+J133okQQsWPx4BQGw9GXNSxQIm692zZsoXp06ezaNEiHnsscpvXBO5i2tnZyeuvv652MI0BfdlNVJHgNDQ0hD22cPXVVzNnzhwWL16M2+2OmA3KHU88lKiTmI0bN/Yqhe1TTz3FsWPH+rTYI1zU6Hj8UbHfacTll19OSUkJzz//PA888ACjR4+OeBtqdDz+pFVP7XA4WLx4cbfHuN1uSkpKYmRR7HnyySfp6OjgmWeeiUr9yh2PP2klapvNRkVFRbfHGAwGSktL+x0znahMnTqV22+/neXLl3Po0KGot6eWc8aetBH14sWLw+6Bi4uLcTgcUbYofjzxxBOcPn2ap59+OuptzZw5k/nz55OXl8f8+fP9lnPu3r2blStX9mpcQNEzaXNPvWbNGurq6vzKioo8YeVtbW3U1dVhMBj09/Lz83E4HFit1oja8eabb3L8+HFaW1sZNWoUo0ePZu7cuX2qq7y8vE/nGY1G7rzzTl599VUef/xxxo8f36d6wiFwyyTw32EFYNeuXeo+O4KkzTz1yJEj9WCNQKqqqmhsbMRut/uVud3uHt313qAFZHR0dLBv3z7y8vIiVndvaW5uZsqUKdx///288MILMW1bBaxEhlDz1GnTU2dlZXUpc7lcOBwOfQlj4PFNTU0RtUETcWBCu3fffZe8vDx2797N97///bDr++CDDwCYPn16r20xGo3ccccdVFVVsWDBAsaNG9frOvqKGiGPLml7OXQ6nZSUlJCfn99nN7av7N27l6FDhwLQ0dEBwKRJk7j22msBaG1tZdOmTT3Ws2XLFj2rZV/42c9+xsmTJ3n22Wf7XEdfUCPk0SVtRN3W1ub3uqGhgdLSUsxmMy5X1/UiLpeL7OzsqNjS0tKiP9+3bx8tLS3s3r2bVatWAbB//3727dtHa2trVNrXOP/887ntttt4+eWX/WyKNSpgJbKkjfttMplwu936YNi8efOwWCzU1tZiMBi6uOdNTU1Rma/u6OjwC/qYPHky+/fvJy8vj8bGRsAz7dTS0qIPJEWTxx9/nNWrV/Pcc8+xaNGiqLcXDOWOR5a06alLS0tZu3at/tpgMNDU1ERtbS3V1dV+g2Tg6ckjPfINMHTo0LBHu6PdU4PnAlJSUsKyZcu6eDOxQrnjkSVtRF1WVtZFuKGIxlRWKPbs2UNLSwsdHR20trbS0dHB0KFDOX78uH6/HW1+/vOf8/XXX7N06dKYtNcTyh3vH2kzpQUesTqdzm6nqdxuN5WVlWFfAOLJyZMnARg8eHC/65o7dy719fXs3bvXb74+HqjlnOGh1lMrusXpdGKxWCK+3joSLF++nN27dzNq1ChaW1u58MILufjii9N+Xlutp05BNmzYwIYNGyJSl9lspqioiBdeeIETJ05EpM5IEeiOnzx5UoWZdoMSdRLT2Nioj5hHgoqKCr744gt9ai1RCIwfHzx4sBpI64a0mdJS9Mzs2bMxm80sWbKEu+66iwEDBsTbJKBr/LiUkm3btgH4rfzasGFD2rvkoESt8EEIQWVlJaWlpfzhD3/o80KTaKMS+XVPel7KFCG59dZbyc3NxWazkaiDqCqRX/coUSv8GDBgAI888ggffvhhUg1AqbntMyTllJYQogXYF287FAnHcCAT0IbvRwGdwACgFfgqTnZFi8lSyi4bzSWlqBUKRWiU+61QpBhK1ApFiqFErVCkGErUCkWKkZTBJ6NGjZI5OTnxNkOhiCuNjY2twUa/k1LUOTk5Kum8Iu0RQgSd1lXut0KRYihRKxQphhK1QpFiKFErFClGWonaN5Wt2+3GYrF0OSbVU9kqkp+mpiZ+8YtfhHw/KUe/+4rNZguaYscX31S2NpstRpYpFKE5cOAAq1ev5vDhw/zpT3/yTT5xXrDj00bUvU1lG6+N7RXpTXt7Ox9++CFSSt544w327NmD0+nk9OnTDBw4kEmTJlFWVkZnZyevvvpq0DrSRtTBUtm6XC7Ky8tpaGggPz/fb1vgaKWyVSh8aW9vp7GxkcGDB/Paa6+xfft2Pv30Uzo7O8nIyODiiy/mZz/7GQcOHGDChAkMHDiQwsJC6uvrQ9aZNqJ2uVxB97PWhFxUVOQnYovFgtPpVKJWRJT29nZ27NjB8OHDefXVV/nwww/56KOP+O677wCYMmUKV155JUajkcmTJ/P000+zefNmvw6po6OD2bNns3Dhws+DtZE2og6Wyta3rKSkxE/E0Uhlq0g/2tvb2blzJ2PGjGHFihVs27YNp9PJN998A3iynU6bNg2j0UhOTg433nijXy+8efNmpk2bBsA111yjvz7nnHNCtpk2olYook17ezsfffQR11xzDW+//Tatra38/ve/54MPPuCrrzybrowZM4YLL7yQnJwcjEYjN998s5+ItV44UMBammPtb3ekjaiDJX/zLbPb7axYsUJ/Hc1UtorUwFfEf/rTn9iyZQvvvfcezc3N+v/W6NGjmTRpEkajEaPRyK233sr69ev1OkKJGMITcDDSRtSBqWy1Mm2gzGq1Yjab9feilcpWkbz4ivjdd99l69at/M///A979+7lyJEjAJx11llMnjyZgoICFi9ejNvt9uuJv/nmm4iLOJCk3KOsL7m0Fi9ejMFgoKysLKzjLRZLRLNfKJIPXxHX1dWxfft21q1bR3NzM59//jlSSgYOHMjEiRMxGo2UlJTw+eef60kEZs+ezbRp0/Q6wrkf7g1pnyDP7XYze/bssITqcDiora1VwSdphq+IN2zYwM6dO/njH/9Ic3MzBw4coLOzEyEE48ePx2g0MnfuXFpbWxk40OPwXnXVVQwbNiwqAg5G2osaUi+VraLv+Ap48+bNXHrppfzud79jzZo1NDc3s2/fPj1V8Lhx4/RBrWPHjnHWWWcBsRdxIErUirQmUMRff/217ko3Nzdz6NAhvvzySwCys7MxGo3cdNNNfPXVVwwdOhSIv4gDCSXqtBkoU6QXgSI+fvw47777Lr/61a9obm7m8OHDtLS0AHDOOedwyy23MGHCBDo6OnShFhQUhBRxpAa1ooEStSIlCCbi+vp6XnzxRZqbmzly5AgHDx4EYOjQofzDP/wDQ4cOxWg0kpWVhdVq7XZQK5FFHIhyvxVJR6CANTGuW7eOffv20dzcTGtrK3/7298AGDx4MBaLheHDh2M0Ghk7dixXX311QrnSfUHdUyuSlmC98NatWzl16hQHDhxASsn//d//sW3bNqSUDBgwgGnTpmEwGDAajZx33nlMnz496UUciBK1ImnZtGkTdXV1dHZ26vPAdXV17N+/n87OTgYMGMDUqVMZOXIkJpOJiRMncs0116SciANRA2WKpEHrmadPn84bb7zB4cOH+a//+i+/aaaxY8dSUFCA0WjkjjvuYPr06SlxPxwJ4i5qIYQBMGkPKeVib3kZ4AIMUsqa+FmoiDaaiL/3ve/x29/+lq1bt1JXV8fevXvp6OgAPNNMl156KUajkeLiYs4777x+LXpIZeIuamAe4JBS1gghGoUQVUCZt8wphLADStQphO898u9+9zu2bNmCw+GgubmZ9vZ2wDPNNGXKFIxGI0899RRtbW2qFw6TuItaSlkV8NothCjAR8hCCLOU0qm9bmlpIT//zK1EWVlZ2DHditgSOMg1YcIEVq1axTvvvMPevXs5evQoAEOGDNFXMv3TP/0T//u//4sQAvCsplO9cPjEXdQaQogKINSyKLfvi9GjR6u0OwlKoIhbWlqoqamhoqJCny8GzzTT5MmTsVgslJaWsm/fPl3E2dnZWK1Wv55ZET4JIWohhBV/F3s7YNBeSCldgecoEoNAER87doy3336bxx9/XI/c0kaoJ02axH/8x3+QnZ3N559/zoABAwA477zzmDJlinKvI0Tcp7S8grYBbUCWlNLiHTybBzTgGTzzu6dWU1rxI1DE7e3t/Pd//7dfDPXJkyf11UyzZs1CCMGECRMYNGhQ1JcjphNqnlrRJwJF/NVXX+nLEZubmzl48KA+Qj127FhmzJjBwIEDmTx5MmeddVbCLYJIJdQ8taJP7Ny5k+rqamw2W5fVTFrM9ODBg8nJyWHYsGHdili50rFBiVqho/XKRqORX//61zQ3N7Np0yYOHDgAwPDhw7n66qv1keoRI0YoEScgStRpjCbivLw8Xn75ZbZt28bWrVv1aaYRI0ZwxRVXcOmll2IymcjKyup2IYQScWKgRJ1GaCKeNm0av/71r9m2bRsffPABX3zxBeCZK54wYQJmsxmTycTy5cs5fvy4Cr9MMtRAWQqjiTg/P5+qqiq2bdvG5s2bOXToEKdPn2bQoEGMHz+enJwcTCYTP/rRj3j//ff182fPnq2Em8CogbIUJ3DTPCkla9asoba2lgMHDnDq1CkyMjI499xzmT59Okajkdtvv52//vWveh0nT57ssn2tIvlQok5SfEW8adMmPv30U/7whz/om+Z9++23gCcjhMVi0UX84Ycf6nV0dnZGfQ9qRexRok5CpJSsW7eO1atX8y//8i80Nzfrc8UjR47k4osvpqKigiFDhuB06iHzZGRkKBGnAUrUScKePXtYvXo1Bw8e5C9/+YseQ3322Wdz/vnnc8MNN3DixAlGjBgBeEIvp02bxsiRI5WI0wwl6gRl7969rFq1isOHD/PnP/+Z/fv3A54R6pycHGbMmMGYMWPIzs5GCBFyvlitbko/IipqIUQOcC9gBiSe1VUuYI2Ucmck20o1Pv/8c1avXs2RI0d45513+Nvf/oaUkkGDBjF58mTuu+8+Tp06xbhx4xBC8PDDD/Pxxx+rXljRhYiJWghxDzACsEspm33KRwDzhBBWKeWzkWovmWlvb2f79u0MGDCA119/nc8++4zt27frq5kmTpzInXfeiZSS8ePHM2DAAAoLC/0SrX388ceqF1YEJZI9tcNXzBpSyi+BFQBCiHOklO0RbDNpOHXqFE6nk/r6et5++2127tzJqVOnEEIwdepUHn30UQ4dOsTEiRMZNGhQFxEHS3mqUAQjYqIOJmivO96mCTmdBC2l5JNPPqG+vp733nuPjRs3cvz4cQAuuugiLBYLOTk55OTksGjRIjZv3kxdXZ1+fjTyFivSg6gMlAkhFgFrgMXAMaA0Gu0kElJKXC4X9fX11NXVsX79ev7+978DMH78eC688EKMRqMu5NbWVv1c355XiVjRX6I1+p2LR8iVQHmU2og7n3/+OevXr9eFvG/fPgDOPfdcrr/+egoLCyksLGTSpEksXLhQP+/2228POsil7pEVkSBaoq7Fs2PJDiFEymRub2trY8OGDdTX11NfX8/u3bsBT8DHrFmzqKiooLCwkAsvvFDfbws8m9H7oga5FNEkKqKWUq4I9jzZ+Prrr/V73fr6enbs2IGUkqFDhzJjxgzuuusuCgsLufzyy8nIyAhZTzDXWqGIFhFbpSWEeAb4ZajBMCHE3cDaSAyWRWuV1rfffsvWrVt1d3rbtm2cOnWKwYMHc9VVVzF79mwKCwu58sorGTx4cMTbVyh6Q9RXaUkpHxNCPCOEMOLZRLAJGIVnV1AJVCba6HdnZ6c+zVRXV8fmzZv55ptvyMjIwGKx8Mgjj1BYWMj3vvc9PfG4QpHoRNT9llI+BnrAiQlweeepEwIpJbt27dLd6Q0bNuj7bV1yySXcc889zJ49mxkzZmAwGOJrbALw3XffcfDgQU6cOBFvU9KazMxMfTfWcIjWQNlsKeXvolR32EgpaW5u1nvi+vp6fZrJZDJRUlLC7NmzmTVrFmPHjo2ztYnHwYMHGT58ODk5OX4Df4rYIaXk6NGjHDx4EKPRGNY50RJ1ARAXUR8+fFgfnfadZho3bhxFRUX6NFNOTk48zEsqTpw4oQQdZ4QQZGdn09LSEvY50RK1xTsw1oYnfDRq99LHjh1jw4YNek/sO800c+ZMHn30UWbNmkVeXp765+wD6juLP739DaIlaqeU8hXvoNk84JXuDvZm6SiSUlb6lPWYylZKyYUXXkhLSwtDhw7l2muv5c4779SnmbS0LgpFMuByuXC5XFit1n7VEy1Rr/Eu3mimB0EDSCkdQgg98sybLK/HVLZCCGxLbbx27DXevv1tRp8zOmIfQBEfXC4XRUVF+j+2wWDAZrP1ub6ioiJqa2t7fZ7D4cDlckUlm6rD4SArKwuXy4XBYMBkMuFyuXC73RERdeiIiX4gpdzRT5e7AJ9Ml0IIc6gDB148kE2tm3h377v9aE6RSJhMJux2O3a7HZvNhsPhYPHixQC43W79ON/nyURtbS0GgwGz2UxWVhZ2u52srCxMJhNms7nfnysqoo4Cbt8XWn7q/Px87nvlPgBW7lgZD7sUXtrb29m0aRNSSjZt2qQnj48EVquViooKACor9Ts0v+fJRGlpqd4zNzQ0UFpaSltbGyaTCafTSVtbW7/qT9TtjLpNZbv/u/3s/0fP9j6DBwyGTvjrgb8iFp4ZUJhtnI3jDkdsrFXw0UcfUVdX57d8tK9x7Q0NDZSXe+7GSko8KctdLhdNTU04HA5dzNrz8vJyvay8vFyfrszPz8flCp4FuaSkhBUrVmAwGCgqKtI9A7fbrbetteF0OqmoqNBdeZfL5deey+WitrYWk8nU5VbB6XSyZs0anE4nZrOZgoICiouL9ffNZn8nVLt49YeEELV3oMwkhDBLKZ1AFZ7dUsCzOMSPDJHBaU4DcLLzpN9fgKGDhvLzGT+PvuEKnWuuucZP0Ndcc02f68rPz8dut+uvHQ7PxXnBggW43W5sNhtut1t/Xl5eTlZWFgaDAbvdjslkYsWKFZjNZiwWS9A2ysvLWbt2LVarVc9IotVbWVmpX0yCYbPZurRnMpkoLe26wlirt6qqirKyMqqqqnA4HNhsNiorK3E6nRQXF+v304Cf6PtCQohaSukALD6v3XiEDeAMPP78rPM5OOggHd91dKlr6KCh/Pm2PzMzZ2Z0jFUEZfPmzV1ex3IFWmVlJSaTSX/eE1arlaKiIpqamigvL9d7VCCk++tb7tseeHrkyspKXeQaBoMBl8tFVlaW3q7JZKK6ulp/7nQ69YtLKM+iNySEqHvL8LOGs6Z4DSXVJZw4dSaEMXNgJmuK1yhBx4FYrETTBFJZWYnNZvN7fs8995CVlUVubi7l5eWUlJT0OIqsichkMlFTU6M/1wQIHq8h0KUObM9gMNDY2IjBYPA7V8PhcDBv3jwAP8Frr00mE5WVlbhcLlasiMCiRill0j0sFotc9dEqefYvz5YZCzPkkKeGyIyFGfLsX54tV320Sioiw65du+JtQspSVlamP29qatKf2+32oMcH+y2ABhlEH8ky+t2FV52v0nGyg2ljp/GHH/6BaWOn0XGyQ42CKxIeLchEc7UdDoc+INffOWpIUvcbYETmCJZcv4SHrnqIDJFBobGQpVuXsmn/pp5PVijiiMlk8guIiXSAS9KK+vc//L3f6wEZA/jp9J/y0+k/jY9BCkWCkLTut0KhCI4StULRC1wulz5vnqgkrfutSE20BR1aQAbgF4jie4zvoFLgMf0hcMFFbW0t2dnZFBcX43Q6I7LoIpqonlqRcJjNZmw2G3a7HYPBQE1N10V6vos+Iilo8F9wYbVayc7O1qPOervowuVy+YWdhiqLJErUioTF5XLpMdORIhzX2XfBhcPhwGw2U11djdPp7NWiC7fbTU1NDb473wYrizQR2yI4lkRri2CFP7t37yYvLw+Ahx56iJ07d0ak3ssvv5ylS5cGfc/XtV67di2NjY1dorBcLhcWi0WP0rJYLGFPC2mutXah6GnBRU9oF55AtJ5ds6+x0T+nhW9ZVVVVyAUhGr6/hUbUtwhWKCKF2WzGbrdjsVhwOBxBBRu46COQUGID9NBSLfa6PwsuNJe8PzQ1NYVcENIXlKgVYRGqZ40mZWVlveqFfQkltsDdRfq74CKcnronbDZbyAUhfSJY7GiiPywWS/eBtYqIEI/Y76amJllcXKy/ttvt0m63y2PHjsmKigr9GIPBIIuLi/XHsWPH/I4JRbDYaq1+X3xjs6WUsqKiQm8nXDR7DAaDtNlsIcvsdrssKyvrtv7exH7HXaB9eShRx4Z0XtDR2wUX0aY3olbut0IRgO+CC5PJhMPh0JdkJvL8tIYStUIRQLQXXEQbNU+tUKQYStSKiPHliS+55be38OWJhMmJmJYoUSsixjufvcPvP/s9f/zfP8bblLRGiVoRMbRdZ/q7+4zb7aakpETfayzYZnzhHJOuqIEyRZ+xvmGlrvnMtsCDBwwG+r8H++zZs6muru42CCOcY+KFts0w9C6ENVKonlrRZx6/9nGGDhqqv47EHuwOh4P8/PxuxRrOMd2dG20WLVpEeXk5drud6urqqLcXiOqpFX1mlnEWf/qnP3HjWzdGbA92l8tFbm5uv4/pjsCVX4GLOtra2igtLe02/ttsNocMD83OzvZbxaVtrNDToo1IoUSt6BezjLMiuge7Fnfd32PCXdCh1ee7qEMLOuku/ru7hRxlZWWUlJToKXqysrIivmijOxJW1OHkp1YkBu4TbgZmDCRDZHDWgLP4tvNbBmYMxH3C3eu6rFarvrF9KNGEc0y4Czqg66KOcDbc72khhxa84nQ69XS8EV200R3BYkfj/QAqALP3uT3wfRX7HRvCjf2e+dpMmfGLDHnFr6+Q7/3tPXnFr6+QGb/IkLNen9Wndo8dOyaLi4v1RQ6NjY1dFmuEc0wwQsVu97Soozfx301NTbpd2nnhLNrojqRf0AFUAybvc7smcO0xadIkabFY9Ee8guxTnXBF/YO3fiB/9cGvZOfpTimllKc6T8ln//qs/MFbP4iiddGlqalJWq1WP1HW1tbKxsZGP4HHit6IOiF3PhFCVAOVUkqXEMIO2KRPOlu180lsCLbbhiI+9Gbnk0Sd0uo2P7VCoQhNog6UdZufWhE7pJR4fwdFnOitN52QopY95KdWxIbMzEyOHj1Kdna2EnackFJy9OhRMjMzwz4nIUWtSAwmTJjAwYMHaWlpibcpaU1mZiYTJkwI/4Rgo2eJ/gic0krW0W9ld2xJRru7s5lUy0/tS1VVVc8HJSDK7tiSjHb3xeaUELVCoThDQs5T94QQ4iTwnU/RQOBUnMzpD8ru2JKMdndn8yAp5eDAwqQUtUKhCI1yvxWKFEOJWqFIMZSoFYoUI+mDT5Jx3bUQwgoUSSkr421LuAghDIBJe0gpF8fXovDxft8GgGT5H9EQQpjxfN9h253UPbUQogLPBLwDKIq3PeHitTfxdszrnnmA2/vPVeoVecLjFYV2wV8Qb3v6gBXI6s0JSS1qoABway+8P6AiCkgpq6TPajnpic9PeKSUTsDh9egWxdue3uD1MHq9U2KyizoQd7wNSHW83lFJvO3oDd4LkAOI/gZhEUIIYfZ6dL0m2UWt1l3HEG/PkWz3pBVCCJP3f8OULLcNoH/fVsDSG7uTfaAsKddde38sk/dqnBRLS70224A2PPd4lvhaFDY1gEEIUQysSbLbBoQQvR4rUhFlCkWKkezut0KhCECJWqFIMZSoFYoUQ4la0W+EEEGTQwkhTN75YUUMUaJW9AuvoIMGdXinkQxCiGSLnktqlKgV/cXUwzRRDVAeI1sUJP88tSKCeMNsSwEznq2Zt+OZk3YBrsDgHm9ARJvP6zI8MfgubbGK9GRZUeG7MUSJWuGLS0pZKYQok1JWed1mkxauGPgaz6KUJp/zc/FcANbE1GqFH0rUCh0ppdsrXK33NeOJfPMtM3FmkYELyPY5v9LbK9uEEOU+Pbs76sYrdJSoFYFYgbXe5048gmzwlrsAtxDCIKV0ey8CBu1Er/tt8Z7T5i0zeM9TxAglaoUfUkrfjaa1TRHaONND6+Lu4VyNeSh3PKao2G9Fv/D2xPNCCBohREUy7ZKSCihRK/qN5o6HW66ILkrUCkWKoYJPFIoUQ4laoUgxlKgVihRDiVqhSDGUqBWKFEOJWqFIMf4/m5hOdQKtAyQAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 237.6x288 with 2 Axes>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig.savefig(\"plots/final/taylor_scale_methods.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Meta-analysis: dependence on t_max. Takes ~ 4min to run\n",
    "\n",
    "# tau_max_lower = 20\n",
    "# tau_max_upper = 1000\n",
    "\n",
    "# tau_fit_max = np.arange(tau_max_lower, tau_max_upper +1)\n",
    "# tau_ts_meta = np.array([])\n",
    "\n",
    "# for i in tau_fit_max:\n",
    "#     ts_est_final = compute_taylor_chuychai(time_lags_hr, r_vec_hr, tau_min=10, tau_max=i, q = -2.14, show = False)\n",
    "#     tau_ts_meta = np.append(tau_ts_meta, ts_est_final)\n",
    "\n",
    "# plt.plot(tau_fit_max, tau_ts_meta)\n",
    "# plt.xlabel(\"$\\\\tau_{max}$\")\n",
    "# plt.ylabel(\"$\\\\tau_{final}$\")\n",
    "# plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These settings can be investigated by looking at the output plots of the `calculate_numerical_vars.py` script. These show the ACFs and fits for the min, median and max correlation scale (exp method) and Taylor scale."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Spectrum comparison for intervals with different energies\n",
    "This is the update to the spectrum \"cartoon\" which demonstrates the important of the Taylor scale Re in capturing the different energies (fluctuation amplitudes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyError",
     "evalue": "\"['di'] not in index\"",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "Input \u001b[1;32mIn [40]\u001b[0m, in \u001b[0;36m<cell line: 5>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      2\u001b[0m timestamp_1 \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m1996-10-15 00:00:00\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m      3\u001b[0m timestamp_2 \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m2004-02-28 12:00\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m----> 5\u001b[0m \u001b[43mdf_wind\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mloc\u001b[49m\u001b[43m[\u001b[49m\u001b[43m[\u001b[49m\u001b[43mtimestamp_1\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtimestamp_2\u001b[49m\u001b[43m]\u001b[49m\u001b[43m]\u001b[49m\u001b[43m[\u001b[49m\n\u001b[0;32m      6\u001b[0m \u001b[43m    \u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mtcf\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mdi\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mdb\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mqi\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mqk\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mtb\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mRe_di\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mRe_tb\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mRe_lt\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mttc\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m]\u001b[49m\n\u001b[0;32m      7\u001b[0m \u001b[43m]\u001b[49m\n",
      "File \u001b[1;32mc:\\Users\\spann\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\pandas\\core\\frame.py:3511\u001b[0m, in \u001b[0;36mDataFrame.__getitem__\u001b[1;34m(self, key)\u001b[0m\n\u001b[0;32m   3509\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m is_iterator(key):\n\u001b[0;32m   3510\u001b[0m         key \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlist\u001b[39m(key)\n\u001b[1;32m-> 3511\u001b[0m     indexer \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcolumns\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_get_indexer_strict\u001b[49m\u001b[43m(\u001b[49m\u001b[43mkey\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mcolumns\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m)\u001b[49m[\u001b[38;5;241m1\u001b[39m]\n\u001b[0;32m   3513\u001b[0m \u001b[38;5;66;03m# take() does not accept boolean indexers\u001b[39;00m\n\u001b[0;32m   3514\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(indexer, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdtype\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;28;01mNone\u001b[39;00m) \u001b[38;5;241m==\u001b[39m \u001b[38;5;28mbool\u001b[39m:\n",
      "File \u001b[1;32mc:\\Users\\spann\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\pandas\\core\\indexes\\base.py:5782\u001b[0m, in \u001b[0;36mIndex._get_indexer_strict\u001b[1;34m(self, key, axis_name)\u001b[0m\n\u001b[0;32m   5779\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m   5780\u001b[0m     keyarr, indexer, new_indexer \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_reindex_non_unique(keyarr)\n\u001b[1;32m-> 5782\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_raise_if_missing\u001b[49m\u001b[43m(\u001b[49m\u001b[43mkeyarr\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mindexer\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis_name\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m   5784\u001b[0m keyarr \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mtake(indexer)\n\u001b[0;32m   5785\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(key, Index):\n\u001b[0;32m   5786\u001b[0m     \u001b[38;5;66;03m# GH 42790 - Preserve name from an Index\u001b[39;00m\n",
      "File \u001b[1;32mc:\\Users\\spann\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\pandas\\core\\indexes\\base.py:5845\u001b[0m, in \u001b[0;36mIndex._raise_if_missing\u001b[1;34m(self, key, indexer, axis_name)\u001b[0m\n\u001b[0;32m   5842\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mKeyError\u001b[39;00m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mNone of [\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mkey\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m] are in the [\u001b[39m\u001b[38;5;132;01m{\u001b[39;00maxis_name\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m]\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m   5844\u001b[0m not_found \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlist\u001b[39m(ensure_index(key)[missing_mask\u001b[38;5;241m.\u001b[39mnonzero()[\u001b[38;5;241m0\u001b[39m]]\u001b[38;5;241m.\u001b[39munique())\n\u001b[1;32m-> 5845\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mKeyError\u001b[39;00m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mnot_found\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m not in index\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "\u001b[1;31mKeyError\u001b[0m: \"['di'] not in index\""
     ]
    }
   ],
   "source": [
    "# Min and max of db. Want to compute the intervals of these.\n",
    "timestamp_1 = \"1996-10-15 00:00:00\"\n",
    "timestamp_2 = \"2004-02-28 12:00\"\n",
    "\n",
    "df_wind.loc[[timestamp_1, timestamp_2]][\n",
    "    [\"tcf\", \"di\", \"db\", \"qi\", \"qk\", \"tb\", \"Re_di\", \"Re_tb\", \"Re_lt\", \"ttc\"]\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def process_get_spectra(file, timestamp):\n",
    "    print(file, timestamp)\n",
    "\n",
    "    df = utils.pipeline(\n",
    "        file,\n",
    "        varlist=sys_arg_dict[\"mag_vars\"],\n",
    "        thresholds=sys_arg_dict[\"mag_thresh\"],\n",
    "        cadence=sys_arg_dict[\"dt_hr\"],\n",
    "    )\n",
    "    # print(\"Reading {0}: {1:.2f}% missing\".format(file, df.iloc[:,0].isna().sum()/len(df)*100))\n",
    "\n",
    "    # Ensuring observations are in chronological order\n",
    "    df_wind_hr = df.sort_index()\n",
    "\n",
    "    df_wind_hr = df_wind_hr.rename(\n",
    "        columns={\n",
    "            params.Bwind: \"Bwind\",\n",
    "            params.Bx: \"Bx\",\n",
    "            params.By: \"By\",\n",
    "            params.Bz: \"Bz\",\n",
    "        }\n",
    "    )\n",
    "\n",
    "    df_wind_hr.shape\n",
    "    int_wind_hr = df_wind_hr[\n",
    "        pd.to_datetime(timestamp) : pd.to_datetime(timestamp)\n",
    "        + pd.to_timedelta(params.int_size)\n",
    "    ]\n",
    "    int_wind_hr.shape\n",
    "\n",
    "    missing = int_wind_hr.iloc[:, 0].isna().sum() / len(int_wind_hr)\n",
    "    print(missing)\n",
    "\n",
    "    if missing > 0.4:\n",
    "        # Replacing values in lists with na\n",
    "        print(\"Large missing %\")\n",
    "    else:\n",
    "        int_wind_hr = int_wind_hr.interpolate().ffill().bfill()\n",
    "\n",
    "    (\n",
    "        z_i,\n",
    "        z_k,\n",
    "        spectral_break,\n",
    "        fig,\n",
    "        ax,\n",
    "        f_periodogram,\n",
    "        p_smooth,\n",
    "    ) = utils.compute_spectral_stats(\n",
    "        np.array([int_wind_hr.Bx, int_wind_hr.By, int_wind_hr.Bz]),\n",
    "        dt=float(params.dt_hr[:-1]),\n",
    "        f_min_inertial=params.f_min_inertial,\n",
    "        f_max_inertial=params.f_max_inertial,\n",
    "        f_min_kinetic=params.f_min_kinetic,\n",
    "        f_max_kinetic=params.f_max_kinetic,\n",
    "        plot=True,\n",
    "    )\n",
    "\n",
    "    return z_i, z_k, spectral_break, f_periodogram, p_smooth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data/spare_data/1996/wi_h2_mfi_19961015_v05.cdf 1996-10-15 00:00:00\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.008940170284901378\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "posx and posy should be finite values\n",
      "posx and posy should be finite values\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 237.6x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z_i1, z_k1, spectral_break1, f_periodogram1, p_smooth1 = process_get_spectra(\n",
    "    \"data/spare_data/1996/wi_h2_mfi_19961015_v05.cdf\", timestamp_1\n",
    ")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data/spare_data/2004/wi_h2_mfi_20040228_v05.cdf 2004-02-28 12:00\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.008535577684831035\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 237.6x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z_i2, z_k2, spectral_break2, f_periodogram2, p_smooth2 = process_get_spectra(\n",
    "    \"data/spare_data/2004/wi_h2_mfi_20040228_v05.cdf\", timestamp_2\n",
    ")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_wind[\"f_cf\"] = 1 / (df_wind[\"tcf\"] * 2 * np.pi)\n",
    "df_wind[\"f_di\"] = df_wind[\"vsw\"] / (df_wind[\"di\"] * 2 * np.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 237.6x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(3.3, 2))\n",
    "ax.set_ylim(1e-6, 1e8)\n",
    "ax.set_xlim(1e-5, 5)\n",
    "\n",
    "ax.semilogy(f_periodogram1, p_smooth1, color=\"black\")\n",
    "ax.semilogy(f_periodogram2, p_smooth2, color=\"gray\")\n",
    "ax.semilogx()\n",
    "ax.set_xlabel(\"$\\log(k)$\")\n",
    "ax.set_ylabel(\"$\\log(E(k))$\")\n",
    "ax.axvline(df_wind.loc[timestamp_1, \"f_di\"], color=\"black\")\n",
    "ax.axvline(df_wind.loc[timestamp_2, \"f_di\"], color=\"gray\")\n",
    "# ax.axvline(5e-1, label = \"$\\lambda_d$\", color='black', alpha = 0.6)\n",
    "ax.axvline(df_wind.loc[timestamp_1, \"f_cf\"], color=\"black\")\n",
    "ax.axvline(df_wind.loc[timestamp_2, \"f_cf\"], color=\"gray\")\n",
    "ax.text(2e-4, 1e-5, \"$\\lambda_C$\")\n",
    "ax.text(2e-1, 1e-5, \"$d_i$\")\n",
    "ax.text(\n",
    "    2e-3,\n",
    "    1e6,\n",
    "    \"$Re_{{d_i}}={0:.0f}$\".format(round(df_wind.loc[timestamp_2, \"Re_di\"], -3)),\n",
    "    color=\"gray\",\n",
    ")\n",
    "ax.text(\n",
    "    2e-3,\n",
    "    1e5,\n",
    "    \"$Re_{{d_i}}={0:.0f}$\".format(round(df_wind.loc[timestamp_1, \"Re_di\"], -3)),\n",
    "    color=\"black\",\n",
    ")\n",
    "ax.text(\n",
    "    2e-3,\n",
    "    5e-3,\n",
    "    \"$Re_{{\\lambda_T}}={0:.0f}$\".format(round(df_wind.loc[timestamp_2, \"Re_lt\"], -3)),\n",
    "    color=\"gray\",\n",
    ")\n",
    "ax.text(\n",
    "    2e-3,\n",
    "    5e-4,\n",
    "    \"$Re_{{\\lambda_T}}={0:.0f}$\".format(round(df_wind.loc[timestamp_1, \"Re_lt\"], -3)),\n",
    "    color=\"black\",\n",
    ")\n",
    "\n",
    "ax.set_xticks([])\n",
    "ax.set_xticks([], minor=True)\n",
    "ax.set_yticks([])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig.savefig(\"plots/final/spectrum_comparison.pdf\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.4 64-bit",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.4"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "690c7be24fab4b896e6241006c45e576997b24f388f83156a67f10121b6b03e9"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}