nb_salinitymodel01_precprocessing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "statewide-satisfaction",
   "metadata": {},
   "source": [
    "# Salinity Setup <br> Data Preprocessing\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "neutral-guinea",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import xarray as xr\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "gorgeous-south",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "## Features\n",
    "***\n",
    "**Outline**  \n",
    "[Principal Component Analysis](https://towardsdatascience.com/pca-using-python-scikit-learn-e653f8989e60 \"Towards Data Sciene | PCA using Python (scikit-learn)\") & \n",
    "[Data loading & preprocessing](https://keras.io/getting_started/intro_to_keras_for_engineers/#data-loading-amp-preprocessing \"Keras\") \n",
    "1. Load and normalize data\n",
    "2. Apply PCA transformation\n",
    "3. Normalize principal components"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "closed-message",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "### 1. Loading & Normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "appreciated-script",
   "metadata": {},
   "outputs": [],
   "source": [
    "feat = xr.merge([\n",
    "    xr.open_dataset('data/da_pred_all.nc'),\n",
    "    xr.open_dataset('data/da_pred_salinty.nc')\n",
    "]).to_dataframe()\n",
    "\n",
    "feat_unit = pd.DataFrame(\n",
    "    data = StandardScaler().fit_transform(feat), \n",
    "    columns = feat.columns,\n",
    "    index =  feat.index\n",
    ")\n",
    "\n",
    "# print(feat_unit.mean())\n",
    "# print(feat_unit.std())\n",
    "# display(feat_unit)\n",
    "# display(feat_unit.describe())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "incident-signature",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "### 2. PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "global-cheat",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Scikit pca transformation\n",
    "pca = PCA().fit(feat_unit)\n",
    "\n",
    "pca_components = pd.DataFrame(\n",
    "    data = pca.components_\n",
    ")\n",
    "\n",
    "feat_pc = pd.DataFrame(\n",
    "    data = np.dot(feat_unit, pca_components.T), # already centered '- pca.mean_' not necessary\n",
    "    columns = [f'PC{i}' for i in range(1, len(feat_unit.columns)+1)],\n",
    "    index =  feat.index\n",
    ")    \n",
    "\n",
    "# print(feat_pc.mean())\n",
    "# print(feat_pc.std())\n",
    "# display(feat_pc)\n",
    "# display(feat_pc.describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "handmade-marker",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>siod_e</th>\n",
       "      <th>siod_w</th>\n",
       "      <th>sst_med</th>\n",
       "      <th>tsa</th>\n",
       "      <th>tna</th>\n",
       "      <th>sst_mdr</th>\n",
       "      <th>sata_lnh</th>\n",
       "      <th>sata_lsh</th>\n",
       "      <th>sata_onh</th>\n",
       "      <th>sata_osh</th>\n",
       "      <th>...</th>\n",
       "      <th>amo</th>\n",
       "      <th>nao</th>\n",
       "      <th>pdo</th>\n",
       "      <th>np</th>\n",
       "      <th>nino12</th>\n",
       "      <th>nino3</th>\n",
       "      <th>nino34</th>\n",
       "      <th>nino4</th>\n",
       "      <th>sssa_na</th>\n",
       "      <th>sssa_sa</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>year</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1901</th>\n",
       "      <td>-1.100027</td>\n",
       "      <td>-1.152764</td>\n",
       "      <td>-0.745530</td>\n",
       "      <td>-0.595366</td>\n",
       "      <td>0.388372</td>\n",
       "      <td>0.608415</td>\n",
       "      <td>-0.123443</td>\n",
       "      <td>-0.732091</td>\n",
       "      <td>-0.497808</td>\n",
       "      <td>-0.737797</td>\n",
       "      <td>...</td>\n",
       "      <td>0.923204</td>\n",
       "      <td>0.917456</td>\n",
       "      <td>-0.193321</td>\n",
       "      <td>1.938388</td>\n",
       "      <td>-0.950168</td>\n",
       "      <td>-0.595561</td>\n",
       "      <td>-0.214314</td>\n",
       "      <td>-0.079270</td>\n",
       "      <td>0.655532</td>\n",
       "      <td>0.602499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1902</th>\n",
       "      <td>0.088643</td>\n",
       "      <td>0.340415</td>\n",
       "      <td>-1.507314</td>\n",
       "      <td>-0.954566</td>\n",
       "      <td>-0.346586</td>\n",
       "      <td>-0.173588</td>\n",
       "      <td>-1.289978</td>\n",
       "      <td>-0.201810</td>\n",
       "      <td>-1.175314</td>\n",
       "      <td>-0.987096</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.620146</td>\n",
       "      <td>-1.172590</td>\n",
       "      <td>0.819716</td>\n",
       "      <td>-0.162154</td>\n",
       "      <td>0.991321</td>\n",
       "      <td>0.969845</td>\n",
       "      <td>1.099218</td>\n",
       "      <td>1.070532</td>\n",
       "      <td>0.634311</td>\n",
       "      <td>0.258427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1903</th>\n",
       "      <td>-0.900789</td>\n",
       "      <td>0.669332</td>\n",
       "      <td>-2.243639</td>\n",
       "      <td>-2.186294</td>\n",
       "      <td>-0.101970</td>\n",
       "      <td>0.283583</td>\n",
       "      <td>-1.333183</td>\n",
       "      <td>-1.076056</td>\n",
       "      <td>-1.415719</td>\n",
       "      <td>-1.333946</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.458290</td>\n",
       "      <td>-1.030410</td>\n",
       "      <td>-0.186187</td>\n",
       "      <td>0.530864</td>\n",
       "      <td>-0.371251</td>\n",
       "      <td>0.000784</td>\n",
       "      <td>0.524139</td>\n",
       "      <td>0.842095</td>\n",
       "      <td>0.043850</td>\n",
       "      <td>0.471247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1904</th>\n",
       "      <td>-0.949568</td>\n",
       "      <td>-1.056219</td>\n",
       "      <td>-0.079925</td>\n",
       "      <td>-1.975498</td>\n",
       "      <td>-2.214111</td>\n",
       "      <td>-1.894743</td>\n",
       "      <td>-1.135674</td>\n",
       "      <td>-1.133384</td>\n",
       "      <td>-1.863746</td>\n",
       "      <td>-1.778347</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.872482</td>\n",
       "      <td>1.447076</td>\n",
       "      <td>-0.892459</td>\n",
       "      <td>0.756497</td>\n",
       "      <td>-0.307712</td>\n",
       "      <td>-0.234313</td>\n",
       "      <td>-0.475713</td>\n",
       "      <td>-0.741738</td>\n",
       "      <td>0.530848</td>\n",
       "      <td>0.575278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1905</th>\n",
       "      <td>-0.034350</td>\n",
       "      <td>-0.632249</td>\n",
       "      <td>-0.718895</td>\n",
       "      <td>-1.684676</td>\n",
       "      <td>-1.334312</td>\n",
       "      <td>-1.014906</td>\n",
       "      <td>-1.314666</td>\n",
       "      <td>-0.595938</td>\n",
       "      <td>-1.284589</td>\n",
       "      <td>-0.954579</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.499163</td>\n",
       "      <td>-1.289888</td>\n",
       "      <td>0.545055</td>\n",
       "      <td>-0.326007</td>\n",
       "      <td>1.227830</td>\n",
       "      <td>1.497381</td>\n",
       "      <td>1.439037</td>\n",
       "      <td>1.032459</td>\n",
       "      <td>0.396927</td>\n",
       "      <td>0.532276</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013</th>\n",
       "      <td>1.195941</td>\n",
       "      <td>0.583772</td>\n",
       "      <td>0.639626</td>\n",
       "      <td>1.003018</td>\n",
       "      <td>1.582829</td>\n",
       "      <td>1.303061</td>\n",
       "      <td>1.610929</td>\n",
       "      <td>1.761660</td>\n",
       "      <td>1.567490</td>\n",
       "      <td>1.375820</td>\n",
       "      <td>...</td>\n",
       "      <td>0.555350</td>\n",
       "      <td>1.141389</td>\n",
       "      <td>-0.550024</td>\n",
       "      <td>0.721578</td>\n",
       "      <td>-1.465545</td>\n",
       "      <td>-0.647168</td>\n",
       "      <td>-0.286199</td>\n",
       "      <td>0.034949</td>\n",
       "      <td>-0.461068</td>\n",
       "      <td>1.914087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014</th>\n",
       "      <td>2.023636</td>\n",
       "      <td>1.289688</td>\n",
       "      <td>1.409613</td>\n",
       "      <td>1.354204</td>\n",
       "      <td>0.162384</td>\n",
       "      <td>0.342794</td>\n",
       "      <td>2.036807</td>\n",
       "      <td>1.847651</td>\n",
       "      <td>2.092010</td>\n",
       "      <td>1.700992</td>\n",
       "      <td>...</td>\n",
       "      <td>0.035451</td>\n",
       "      <td>-0.237757</td>\n",
       "      <td>1.094378</td>\n",
       "      <td>-0.100373</td>\n",
       "      <td>0.606553</td>\n",
       "      <td>1.170538</td>\n",
       "      <td>0.948913</td>\n",
       "      <td>1.078147</td>\n",
       "      <td>-0.197876</td>\n",
       "      <td>1.565808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015</th>\n",
       "      <td>2.226665</td>\n",
       "      <td>1.764942</td>\n",
       "      <td>2.001272</td>\n",
       "      <td>1.161939</td>\n",
       "      <td>0.276530</td>\n",
       "      <td>0.362771</td>\n",
       "      <td>2.178766</td>\n",
       "      <td>2.026800</td>\n",
       "      <td>2.518182</td>\n",
       "      <td>1.809382</td>\n",
       "      <td>...</td>\n",
       "      <td>0.092673</td>\n",
       "      <td>1.404422</td>\n",
       "      <td>1.247760</td>\n",
       "      <td>0.281055</td>\n",
       "      <td>1.580828</td>\n",
       "      <td>2.093726</td>\n",
       "      <td>2.255911</td>\n",
       "      <td>2.532532</td>\n",
       "      <td>-1.038432</td>\n",
       "      <td>2.059816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016</th>\n",
       "      <td>2.225848</td>\n",
       "      <td>0.933042</td>\n",
       "      <td>1.586111</td>\n",
       "      <td>1.389252</td>\n",
       "      <td>1.070022</td>\n",
       "      <td>1.482667</td>\n",
       "      <td>2.765120</td>\n",
       "      <td>2.134289</td>\n",
       "      <td>2.714877</td>\n",
       "      <td>2.145393</td>\n",
       "      <td>...</td>\n",
       "      <td>1.609864</td>\n",
       "      <td>-1.279225</td>\n",
       "      <td>2.253663</td>\n",
       "      <td>0.052735</td>\n",
       "      <td>0.465354</td>\n",
       "      <td>0.832227</td>\n",
       "      <td>1.184173</td>\n",
       "      <td>1.717772</td>\n",
       "      <td>-0.929217</td>\n",
       "      <td>2.979758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017</th>\n",
       "      <td>0.267588</td>\n",
       "      <td>2.013635</td>\n",
       "      <td>2.491512</td>\n",
       "      <td>1.488384</td>\n",
       "      <td>1.828710</td>\n",
       "      <td>1.651864</td>\n",
       "      <td>2.283693</td>\n",
       "      <td>2.019634</td>\n",
       "      <td>2.376125</td>\n",
       "      <td>1.917773</td>\n",
       "      <td>...</td>\n",
       "      <td>1.567356</td>\n",
       "      <td>0.668641</td>\n",
       "      <td>0.751943</td>\n",
       "      <td>-1.373592</td>\n",
       "      <td>0.352395</td>\n",
       "      <td>0.660204</td>\n",
       "      <td>0.648304</td>\n",
       "      <td>0.842095</td>\n",
       "      <td>0.883910</td>\n",
       "      <td>2.665707</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>117 rows × 22 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        siod_e    siod_w   sst_med       tsa       tna   sst_mdr  sata_lnh  \\\n",
       "year                                                                         \n",
       "1901 -1.100027 -1.152764 -0.745530 -0.595366  0.388372  0.608415 -0.123443   \n",
       "1902  0.088643  0.340415 -1.507314 -0.954566 -0.346586 -0.173588 -1.289978   \n",
       "1903 -0.900789  0.669332 -2.243639 -2.186294 -0.101970  0.283583 -1.333183   \n",
       "1904 -0.949568 -1.056219 -0.079925 -1.975498 -2.214111 -1.894743 -1.135674   \n",
       "1905 -0.034350 -0.632249 -0.718895 -1.684676 -1.334312 -1.014906 -1.314666   \n",
       "...        ...       ...       ...       ...       ...       ...       ...   \n",
       "2013  1.195941  0.583772  0.639626  1.003018  1.582829  1.303061  1.610929   \n",
       "2014  2.023636  1.289688  1.409613  1.354204  0.162384  0.342794  2.036807   \n",
       "2015  2.226665  1.764942  2.001272  1.161939  0.276530  0.362771  2.178766   \n",
       "2016  2.225848  0.933042  1.586111  1.389252  1.070022  1.482667  2.765120   \n",
       "2017  0.267588  2.013635  2.491512  1.488384  1.828710  1.651864  2.283693   \n",
       "\n",
       "      sata_lsh  sata_onh  sata_osh  ...       amo       nao       pdo  \\\n",
       "year                                ...                                 \n",
       "1901 -0.732091 -0.497808 -0.737797  ...  0.923204  0.917456 -0.193321   \n",
       "1902 -0.201810 -1.175314 -0.987096  ... -0.620146 -1.172590  0.819716   \n",
       "1903 -1.076056 -1.415719 -1.333946  ... -0.458290 -1.030410 -0.186187   \n",
       "1904 -1.133384 -1.863746 -1.778347  ... -1.872482  1.447076 -0.892459   \n",
       "1905 -0.595938 -1.284589 -0.954579  ... -0.499163 -1.289888  0.545055   \n",
       "...        ...       ...       ...  ...       ...       ...       ...   \n",
       "2013  1.761660  1.567490  1.375820  ...  0.555350  1.141389 -0.550024   \n",
       "2014  1.847651  2.092010  1.700992  ...  0.035451 -0.237757  1.094378   \n",
       "2015  2.026800  2.518182  1.809382  ...  0.092673  1.404422  1.247760   \n",
       "2016  2.134289  2.714877  2.145393  ...  1.609864 -1.279225  2.253663   \n",
       "2017  2.019634  2.376125  1.917773  ...  1.567356  0.668641  0.751943   \n",
       "\n",
       "            np    nino12     nino3    nino34     nino4   sssa_na   sssa_sa  \n",
       "year                                                                        \n",
       "1901  1.938388 -0.950168 -0.595561 -0.214314 -0.079270  0.655532  0.602499  \n",
       "1902 -0.162154  0.991321  0.969845  1.099218  1.070532  0.634311  0.258427  \n",
       "1903  0.530864 -0.371251  0.000784  0.524139  0.842095  0.043850  0.471247  \n",
       "1904  0.756497 -0.307712 -0.234313 -0.475713 -0.741738  0.530848  0.575278  \n",
       "1905 -0.326007  1.227830  1.497381  1.439037  1.032459  0.396927  0.532276  \n",
       "...        ...       ...       ...       ...       ...       ...       ...  \n",
       "2013  0.721578 -1.465545 -0.647168 -0.286199  0.034949 -0.461068  1.914087  \n",
       "2014 -0.100373  0.606553  1.170538  0.948913  1.078147 -0.197876  1.565808  \n",
       "2015  0.281055  1.580828  2.093726  2.255911  2.532532 -1.038432  2.059816  \n",
       "2016  0.052735  0.465354  0.832227  1.184173  1.717772 -0.929217  2.979758  \n",
       "2017 -1.373592  0.352395  0.660204  0.648304  0.842095  0.883910  2.665707  \n",
       "\n",
       "[117 rows x 22 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feat_unit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "respiratory-contrast",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC1</th>\n",
       "      <th>PC2</th>\n",
       "      <th>PC3</th>\n",
       "      <th>PC4</th>\n",
       "      <th>PC5</th>\n",
       "      <th>PC6</th>\n",
       "      <th>PC7</th>\n",
       "      <th>PC8</th>\n",
       "      <th>PC9</th>\n",
       "      <th>PC10</th>\n",
       "      <th>...</th>\n",
       "      <th>PC13</th>\n",
       "      <th>PC14</th>\n",
       "      <th>PC15</th>\n",
       "      <th>PC16</th>\n",
       "      <th>PC17</th>\n",
       "      <th>PC18</th>\n",
       "      <th>PC19</th>\n",
       "      <th>PC20</th>\n",
       "      <th>PC21</th>\n",
       "      <th>PC22</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>year</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1901</th>\n",
       "      <td>-1.448100</td>\n",
       "      <td>-0.988055</td>\n",
       "      <td>-1.831115</td>\n",
       "      <td>-0.093303</td>\n",
       "      <td>-1.216952</td>\n",
       "      <td>1.326158</td>\n",
       "      <td>-0.323752</td>\n",
       "      <td>0.603090</td>\n",
       "      <td>-1.621739</td>\n",
       "      <td>-0.371594</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.247502</td>\n",
       "      <td>-0.517041</td>\n",
       "      <td>-0.051968</td>\n",
       "      <td>0.295965</td>\n",
       "      <td>-0.079911</td>\n",
       "      <td>0.315402</td>\n",
       "      <td>0.006896</td>\n",
       "      <td>0.185167</td>\n",
       "      <td>0.182891</td>\n",
       "      <td>0.005946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1902</th>\n",
       "      <td>-0.486753</td>\n",
       "      <td>2.651833</td>\n",
       "      <td>-0.796885</td>\n",
       "      <td>0.328434</td>\n",
       "      <td>2.035607</td>\n",
       "      <td>2.645670</td>\n",
       "      <td>0.100720</td>\n",
       "      <td>0.199712</td>\n",
       "      <td>-1.762942</td>\n",
       "      <td>-0.579130</td>\n",
       "      <td>...</td>\n",
       "      <td>0.438948</td>\n",
       "      <td>-0.092332</td>\n",
       "      <td>-0.411823</td>\n",
       "      <td>0.236401</td>\n",
       "      <td>0.084996</td>\n",
       "      <td>-0.591200</td>\n",
       "      <td>0.006940</td>\n",
       "      <td>0.003806</td>\n",
       "      <td>0.025443</td>\n",
       "      <td>-0.043698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1903</th>\n",
       "      <td>-2.299652</td>\n",
       "      <td>1.634670</td>\n",
       "      <td>-1.287301</td>\n",
       "      <td>-0.172967</td>\n",
       "      <td>1.365117</td>\n",
       "      <td>1.326004</td>\n",
       "      <td>-1.070828</td>\n",
       "      <td>0.762107</td>\n",
       "      <td>-1.725267</td>\n",
       "      <td>0.631677</td>\n",
       "      <td>...</td>\n",
       "      <td>0.332137</td>\n",
       "      <td>-0.782816</td>\n",
       "      <td>-0.242917</td>\n",
       "      <td>0.026456</td>\n",
       "      <td>0.253325</td>\n",
       "      <td>-0.212574</td>\n",
       "      <td>0.016677</td>\n",
       "      <td>0.001932</td>\n",
       "      <td>0.146107</td>\n",
       "      <td>-0.005529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1904</th>\n",
       "      <td>-5.037961</td>\n",
       "      <td>0.375492</td>\n",
       "      <td>0.172603</td>\n",
       "      <td>1.919349</td>\n",
       "      <td>-0.652566</td>\n",
       "      <td>1.491636</td>\n",
       "      <td>0.977128</td>\n",
       "      <td>0.557021</td>\n",
       "      <td>-0.269100</td>\n",
       "      <td>0.615024</td>\n",
       "      <td>...</td>\n",
       "      <td>0.350871</td>\n",
       "      <td>0.362969</td>\n",
       "      <td>-0.519302</td>\n",
       "      <td>0.112982</td>\n",
       "      <td>-0.348566</td>\n",
       "      <td>-0.100952</td>\n",
       "      <td>0.098975</td>\n",
       "      <td>-0.050902</td>\n",
       "      <td>0.239010</td>\n",
       "      <td>0.062627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1905</th>\n",
       "      <td>-1.231468</td>\n",
       "      <td>4.193341</td>\n",
       "      <td>-0.164357</td>\n",
       "      <td>1.642997</td>\n",
       "      <td>0.581816</td>\n",
       "      <td>-0.618450</td>\n",
       "      <td>-1.617789</td>\n",
       "      <td>0.790584</td>\n",
       "      <td>1.324908</td>\n",
       "      <td>-0.266027</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.067894</td>\n",
       "      <td>0.360688</td>\n",
       "      <td>0.226720</td>\n",
       "      <td>-0.205175</td>\n",
       "      <td>-0.138728</td>\n",
       "      <td>-0.398312</td>\n",
       "      <td>0.334514</td>\n",
       "      <td>-0.110083</td>\n",
       "      <td>0.180749</td>\n",
       "      <td>0.099679</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013</th>\n",
       "      <td>3.049350</td>\n",
       "      <td>-3.332021</td>\n",
       "      <td>0.327818</td>\n",
       "      <td>0.484582</td>\n",
       "      <td>-1.179290</td>\n",
       "      <td>-0.464816</td>\n",
       "      <td>0.163545</td>\n",
       "      <td>0.697839</td>\n",
       "      <td>-1.229851</td>\n",
       "      <td>0.888779</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.017882</td>\n",
       "      <td>-1.221180</td>\n",
       "      <td>-0.321761</td>\n",
       "      <td>-0.351936</td>\n",
       "      <td>-0.126933</td>\n",
       "      <td>-0.127789</td>\n",
       "      <td>0.287654</td>\n",
       "      <td>-0.421459</td>\n",
       "      <td>-0.070777</td>\n",
       "      <td>-0.004422</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014</th>\n",
       "      <td>4.914815</td>\n",
       "      <td>-0.727248</td>\n",
       "      <td>1.390861</td>\n",
       "      <td>1.324686</td>\n",
       "      <td>0.482945</td>\n",
       "      <td>0.412985</td>\n",
       "      <td>0.893763</td>\n",
       "      <td>1.265534</td>\n",
       "      <td>0.071366</td>\n",
       "      <td>0.341176</td>\n",
       "      <td>...</td>\n",
       "      <td>0.546703</td>\n",
       "      <td>0.037916</td>\n",
       "      <td>-0.010784</td>\n",
       "      <td>0.458917</td>\n",
       "      <td>0.046646</td>\n",
       "      <td>0.203375</td>\n",
       "      <td>-0.215418</td>\n",
       "      <td>-0.253936</td>\n",
       "      <td>0.044088</td>\n",
       "      <td>0.097449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015</th>\n",
       "      <td>6.591440</td>\n",
       "      <td>1.202165</td>\n",
       "      <td>2.309644</td>\n",
       "      <td>2.114795</td>\n",
       "      <td>-1.207829</td>\n",
       "      <td>0.828209</td>\n",
       "      <td>1.484993</td>\n",
       "      <td>1.590163</td>\n",
       "      <td>-0.177081</td>\n",
       "      <td>0.162024</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.126920</td>\n",
       "      <td>-0.371819</td>\n",
       "      <td>0.385036</td>\n",
       "      <td>0.506442</td>\n",
       "      <td>0.283492</td>\n",
       "      <td>-0.154939</td>\n",
       "      <td>-0.440982</td>\n",
       "      <td>-0.195386</td>\n",
       "      <td>-0.125473</td>\n",
       "      <td>-0.054454</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016</th>\n",
       "      <td>7.025027</td>\n",
       "      <td>-0.815487</td>\n",
       "      <td>0.204453</td>\n",
       "      <td>1.205482</td>\n",
       "      <td>0.771263</td>\n",
       "      <td>-1.058064</td>\n",
       "      <td>0.257640</td>\n",
       "      <td>2.695078</td>\n",
       "      <td>0.174419</td>\n",
       "      <td>0.135014</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.652413</td>\n",
       "      <td>-0.748402</td>\n",
       "      <td>-0.046192</td>\n",
       "      <td>0.435408</td>\n",
       "      <td>0.230018</td>\n",
       "      <td>0.023186</td>\n",
       "      <td>-0.176007</td>\n",
       "      <td>-0.047994</td>\n",
       "      <td>0.201910</td>\n",
       "      <td>0.005108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017</th>\n",
       "      <td>6.436751</td>\n",
       "      <td>-1.525566</td>\n",
       "      <td>-0.987016</td>\n",
       "      <td>1.433688</td>\n",
       "      <td>-0.587300</td>\n",
       "      <td>-0.490887</td>\n",
       "      <td>1.608440</td>\n",
       "      <td>-0.231583</td>\n",
       "      <td>0.904956</td>\n",
       "      <td>0.711081</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.345766</td>\n",
       "      <td>-0.247185</td>\n",
       "      <td>0.025310</td>\n",
       "      <td>-0.480991</td>\n",
       "      <td>0.061885</td>\n",
       "      <td>-0.456047</td>\n",
       "      <td>-0.051878</td>\n",
       "      <td>0.006747</td>\n",
       "      <td>-0.103854</td>\n",
       "      <td>-0.077364</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>117 rows × 22 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           PC1       PC2       PC3       PC4       PC5       PC6       PC7  \\\n",
       "year                                                                         \n",
       "1901 -1.448100 -0.988055 -1.831115 -0.093303 -1.216952  1.326158 -0.323752   \n",
       "1902 -0.486753  2.651833 -0.796885  0.328434  2.035607  2.645670  0.100720   \n",
       "1903 -2.299652  1.634670 -1.287301 -0.172967  1.365117  1.326004 -1.070828   \n",
       "1904 -5.037961  0.375492  0.172603  1.919349 -0.652566  1.491636  0.977128   \n",
       "1905 -1.231468  4.193341 -0.164357  1.642997  0.581816 -0.618450 -1.617789   \n",
       "...        ...       ...       ...       ...       ...       ...       ...   \n",
       "2013  3.049350 -3.332021  0.327818  0.484582 -1.179290 -0.464816  0.163545   \n",
       "2014  4.914815 -0.727248  1.390861  1.324686  0.482945  0.412985  0.893763   \n",
       "2015  6.591440  1.202165  2.309644  2.114795 -1.207829  0.828209  1.484993   \n",
       "2016  7.025027 -0.815487  0.204453  1.205482  0.771263 -1.058064  0.257640   \n",
       "2017  6.436751 -1.525566 -0.987016  1.433688 -0.587300 -0.490887  1.608440   \n",
       "\n",
       "           PC8       PC9      PC10  ...      PC13      PC14      PC15  \\\n",
       "year                                ...                                 \n",
       "1901  0.603090 -1.621739 -0.371594  ... -1.247502 -0.517041 -0.051968   \n",
       "1902  0.199712 -1.762942 -0.579130  ...  0.438948 -0.092332 -0.411823   \n",
       "1903  0.762107 -1.725267  0.631677  ...  0.332137 -0.782816 -0.242917   \n",
       "1904  0.557021 -0.269100  0.615024  ...  0.350871  0.362969 -0.519302   \n",
       "1905  0.790584  1.324908 -0.266027  ... -0.067894  0.360688  0.226720   \n",
       "...        ...       ...       ...  ...       ...       ...       ...   \n",
       "2013  0.697839 -1.229851  0.888779  ... -0.017882 -1.221180 -0.321761   \n",
       "2014  1.265534  0.071366  0.341176  ...  0.546703  0.037916 -0.010784   \n",
       "2015  1.590163 -0.177081  0.162024  ... -0.126920 -0.371819  0.385036   \n",
       "2016  2.695078  0.174419  0.135014  ... -0.652413 -0.748402 -0.046192   \n",
       "2017 -0.231583  0.904956  0.711081  ... -0.345766 -0.247185  0.025310   \n",
       "\n",
       "          PC16      PC17      PC18      PC19      PC20      PC21      PC22  \n",
       "year                                                                        \n",
       "1901  0.295965 -0.079911  0.315402  0.006896  0.185167  0.182891  0.005946  \n",
       "1902  0.236401  0.084996 -0.591200  0.006940  0.003806  0.025443 -0.043698  \n",
       "1903  0.026456  0.253325 -0.212574  0.016677  0.001932  0.146107 -0.005529  \n",
       "1904  0.112982 -0.348566 -0.100952  0.098975 -0.050902  0.239010  0.062627  \n",
       "1905 -0.205175 -0.138728 -0.398312  0.334514 -0.110083  0.180749  0.099679  \n",
       "...        ...       ...       ...       ...       ...       ...       ...  \n",
       "2013 -0.351936 -0.126933 -0.127789  0.287654 -0.421459 -0.070777 -0.004422  \n",
       "2014  0.458917  0.046646  0.203375 -0.215418 -0.253936  0.044088  0.097449  \n",
       "2015  0.506442  0.283492 -0.154939 -0.440982 -0.195386 -0.125473 -0.054454  \n",
       "2016  0.435408  0.230018  0.023186 -0.176007 -0.047994  0.201910  0.005108  \n",
       "2017 -0.480991  0.061885 -0.456047 -0.051878  0.006747 -0.103854 -0.077364  \n",
       "\n",
       "[117 rows x 22 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feat_pc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "quantitative-electricity",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "### 3. Normalize Principal Components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "distinct-lodge",
   "metadata": {},
   "outputs": [],
   "source": [
    "feat_pc = pd.DataFrame(\n",
    "    data = StandardScaler().fit_transform(feat_pc), \n",
    "    columns = feat_pc.columns,\n",
    "    index =  feat_pc.index\n",
    ")\n",
    "\n",
    "# print(feat_pc.mean())\n",
    "# print(feat_pc.std())\n",
    "# display(feat_pc)\n",
    "# display(feat_pc.describe())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "opposite-fellow",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "## Labels\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "weighted-reward",
   "metadata": {},
   "source": [
    "**label:** from Sahelrainfall data serves as validation data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "jewish-system",
   "metadata": {},
   "outputs": [],
   "source": [
    "# load validatoin data (Summer Rainfall over Sahel) \n",
    "labels = np.mean(np.loadtxt(\"data/da_o_sahelprecip19012017.txt\", skiprows=8,)[:,7:10] * 0.01,  axis=1)\n",
    "\n",
    "# eventually normlaize output as well\n",
    "# labels = np.squeeze(StandardScaler().fit_transform(np.reshape(labels, (117,1))))\n",
    "\n",
    "# display(labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "welcome-cookbook",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "## Merge to Xarray DataSet\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "destroyed-simulation",
   "metadata": {},
   "outputs": [],
   "source": [
    "model_data = xr.Dataset(\n",
    "    data_vars=dict(\n",
    "        feat_pc = (['year', 'pc'], feat_pc),\n",
    "        labels = (['year'],labels),\n",
    "        feat_standardized = (['year', 'indices'], feat_unit),\n",
    "        pca_components = (['n_components', 'n_features'], pca_components),\n",
    "    ),\n",
    "    coords=dict(\n",
    "        year = feat_pc.index,\n",
    "        pc = feat_pc.columns,\n",
    "        indices = feat.columns,\n",
    "        n_features = range(22),\n",
    "        n_components = range(22)\n",
    "    )\n",
    ")\n",
    "\n",
    "model_data.to_netcdf('data/da_final_salinitymodel.nc')\n",
    "\n",
    "# display(model_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "alien-double",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "## Explained Vairance\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "linear-minister",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[10, 3], dpi=100)\n",
    "\n",
    "plt.bar(feat_pc.columns, pca.explained_variance_ratio_, width=0.5)\n",
    "\n",
    "plt.xlabel(\"PC\")\n",
    "plt.ylabel(\"Fraction of Variance\")\n",
    "plt.ylim(0, 0.45)\n",
    "\n",
    "plt.tick_params(axis='x',which='minor', labelsize=11)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.savefig('./overleaf/img/salinitymodel_pc_var.pdf', facecolor='w')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "incorporate-commitment",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.90011471867075"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_[:10].sum()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}