{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "view-in-github"
},
"source": [
"![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\")
"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "GAwSQhMS3TK_"
},
"source": [
"This notebook will be used in the lab session for week 1 of the course and provides some hands-on experience applying the lessons to environmental science datasets."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "kS57AUwjmh-J"
},
"source": [
"# (Exercises) Statistical Forecasting\n",
"\n",
"We will be using data from Wilks' book on Statistical Methods for the Atmospheric Sciences"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "spYmkik-3K_i"
},
"source": [
"## Notebook Setup"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"cellView": "form",
"id": "o_x3_GmVcKl9"
},
"outputs": [],
"source": [
"#@title Run this cell to get the python environment set up!\n",
"# Python ≥3.5 is required\n",
"import sys\n",
"assert sys.version_info >= (3, 5)\n",
"\n",
"# Is this notebook running on Colab or Kaggle?\n",
"IS_COLAB = \"google.colab\" in sys.modules\n",
"\n",
"# Scikit-Learn ≥0.20 is required\n",
"import sklearn\n",
"assert sklearn.__version__ >= \"0.20\"\n",
"\n",
"# Common imports\n",
"import numpy as np\n",
"import os\n",
"import pandas as pd\n",
"import pooch\n",
"\n",
"#Data Visalization Import\n",
"from google.colab import data_table\n",
"\n",
"\n",
"# to make this notebook's output stable across runs\n",
"rnd_seed = 42\n",
"rnd_gen = np.random.default_rng(rnd_seed)\n",
"\n",
"# To plot pretty figures\n",
"%matplotlib inline\n",
"import matplotlib as mpl\n",
"import matplotlib.pyplot as plt\n",
"mpl.rc('axes', labelsize=14)\n",
"mpl.rc('xtick', labelsize=12)\n",
"mpl.rc('ytick', labelsize=12)\n",
"\n",
"# Where to save the figures\n",
"PROJECT_ROOT_DIR = \".\"\n",
"CHAPTER_ID = \"classification\"\n",
"IMAGES_PATH = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID)\n",
"os.makedirs(IMAGES_PATH, exist_ok=True)\n",
"\n",
"def save_fig(fig_id, tight_layout=True, fig_extension=\"png\", resolution=300):\n",
" path = os.path.join(IMAGES_PATH, fig_id + \".\" + fig_extension)\n",
" print(\"Saving figure\", fig_id)\n",
" if tight_layout:\n",
" plt.tight_layout()\n",
" plt.savefig(path, format=fig_extension, dpi=resolution)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "gQhMBs1CHqPo"
},
"source": [
"Let's begin by loading relevant data from the cloud. "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"cellView": "form",
"id": "lISPw_EDHtkb"
},
"outputs": [],
"source": [
"#@title And this cell to load the data we'll be using as `A3_df`\n",
"#Loading Wilks' Table A-3 from the course datastore\n",
"csv_path = 'https://unils-my.sharepoint.com/:x:/g/personal/tom_beucler_unil_ch/EXG7Rht55mhPiwkUKEDSI8oBuXNe8OOLYJX3_5ACmK1w5A?download=1'\n",
"hash = 'c158828a1bdf1aa521c61321842352cb1674e49187e21c504188ab976d3a41f2'\n",
"csv_file = pooch.retrieve(csv_path, known_hash=hash)\n",
"\n",
"A3_df = pd.read_csv(csv_file, index_col=0)\n",
"print(\"Here's a data sample. You can copy the row header text from here if you need it later 😉\")\n",
"A3_df.head(5)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "AxNcWHCxG3vI"
},
"source": [
"## **Linear Regression**\n",
"\n",
"The goal for this exercise is to train a linear regression model and a logistic regression model to forecast atmospheric temperature using atmospheric pressure. 🌡 \n",
"\n",
"For the first case, we want to train linear regression to calculate June temperatures (the predictand) from June pressures (as the predictor) in Guayaquil, Ecuador.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "jqI3IRvoXjG0"
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "qGvcGjGrXjG8"
},
"source": [
"**Caption** A beautiful day in Guayacil, Ecuador. Can you predict how hot it will be? 🌞"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "7nkw4g5pI3w4"
},
"source": [
"We can try addressing this question using a [linear regression model](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html) from scikit. \n",
"\n",
"## **Q1) Import the LinearRegression model. Instantiate it and fit it using the A3 dataframes' pressure and temperature.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "sP4qIkhaM1YB"
},
"outputs": [],
"source": [
"# Import the LinearRegression model\n",
"from _______._______ import _______"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "6S5OMx6SVfBk"
},
"outputs": [],
"source": [
"# Instantiate the model\n",
"lin_reg = _______()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "lG5ZjQDEVgYN"
},
"outputs": [],
"source": [
"# Load and reshape the input data\n",
"pressure = _______['_______'].values.reshape(-1,1)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "dmVjMnidNaEC"
},
"outputs": [],
"source": [
"# Load the truth data (i.e., the predictant)\n",
"temperature = _______['_______'].to_numpy().ravel()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "5It7zEtYN1mN"
},
"outputs": [],
"source": [
"# Fit the model\n",
"lin_reg._______(_______, _______)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "znzId7C4T3-x"
},
"source": [
"We now have a linear regression model for the temperature and pressure. Let's make some plots to visualize our data and get a qualitative sense of our model.\n",
"\n",
"## **Q2) Generate a scatter plot with the linear regression plot for our data.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "8ps2eoPhPgd1"
},
"outputs": [],
"source": [
"#Instantiate a figure having size 13,6\n",
"fig, ax = plt.subplots(_______=(_______,_______))\n",
"\n",
"\"\"\"---------------------------------------------------------------------------- \n",
"Let's start by plotting the data points from our dataset\n",
"----------------------------------------------------------------------------\"\"\"\n",
"# Set figure title and axis labels\n",
"fig._______('June Temperature vs Pressure in Guayaquil, Ecuador')\n",
"ax._______(\"Pressure (mb)\")\n",
"ax._______(\"Temperature (°C)\")\n",
"\n",
"# The colors and styles suggested below are not compulsory, but please avoid \n",
"# using the default settings.\n",
"# Make a scatter plot for the pressure (x) and temperature (y). Use color=black,\n",
"# marker size = 100, and set the marker style to '2'.\n",
"\n",
"ax._______(_______, # X values\n",
" _______, # y values\n",
" _______=_______, # Color\n",
" _______ = _______, # Marker size\n",
" _______ = _______) # Marker style\n",
"\n",
"\n",
"'''---------------------------------------------------------------------------- \n",
"Now, let's plot the line we fit to the datapoints\n",
"----------------------------------------------------------------------------'''\n",
"# Make a 100 point numpy array between 1008 and 1014 and store it in reg_x. \n",
"# Reshape it to (-1,1). Hint: numpy has a linear space generator\n",
"reg_x = _______._______(_______, # Start\n",
" _______, # Stop\n",
" _______,# Number of Points\n",
" ).reshape(_______,________) # Reshape to row=sample, col=feature\n",
"\n",
"# Let's produce a set of predictions from our linear space array.\n",
"reg_y = lin_reg._______(reg_x)\n",
"\n",
"# Let's plot the regression line using reg_x and reg_y. Set the color to red and\n",
"# the linewidth to 1.5\n",
"ax.plot(_______, # X\n",
" _______, # y\n",
" _______ = _______, # Color\n",
" _______ = _______) # Linewidth\n",
"\n",
"ax.autoscale(axis='x', tight=True)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "gZoEKrwba9XY"
},
"source": [
"We now have a qualitative verification of our model! Your figure should look similar to this one:\n",
"\n",
"
\n",
"\n",
"Qualitative verifications are nice - but this is not enough! Let's do some quantitative analyses:\n",
"\n",
"## **Q3) Print the slope of our model. Find the F-score, p-value, and $R^2$ statistics for our model.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "SCAF7M07h2BH"
},
"outputs": [],
"source": [
"# Fetch the slope directly from the linear model. Hint: check the attributes \n",
"# section of the linear regression model documentation on scikit.\n",
"slope = lin_reg._______\n",
"slope = float(slope)\n",
"\n",
"# Calculate the F-score and p-value for our dataset.\n",
"# Hint: check the f_regression option in sklearn.feature_selection\n",
"from _______._______ import _______\n",
"fscore, pvalue = _______(_______, # X values\n",
" _______) # y values\n",
"fscore=float(fscore)\n",
"pvalue=float(pvalue)\n",
"\n",
"\n",
"# Fetch the R2 value from the lin_reg model. Hint: r2_score in sklearn metrics\n",
"predicted_temperatures = _______._______(_______)\n",
"from _______._______ import _______\n",
"R_squared = _______(_______, # Ground truth\n",
" _______) # Predictions"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "13A0XmO90iCl"
},
"outputs": [],
"source": [
"# Now we print out the results!\n",
"print(f'The slope of the line is: {slope:.2f}',\n",
" f'The f score is: {fscore:.0f}',\n",
" f'The R\\u00b2 value is: {R_squared:.2f}',\n",
" sep='\\n')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "pQ9GUTVM0mbP"
},
"source": [
"If your code works just the way ours does, you'll get:\n",
"\n",
"The slope of the line is: -0.92 \\\n",
"The f score is: 40 \\\n",
"The R² value is: 0.69"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "HlVgyHB3RHO1"
},
"source": [
"## **Classification**\n",
"\n",
"Let's use the same dataset to train a classifier for El Niño years. \\\n",
"\n",
"**We will use the June temperature and pressure in Guayaquil as the predictors for El Niño.** \\\n",
"\n",
"Let's begin by setting up a training and testing dataset. Since the dataset is so small, we'll set aside one each of a random El Niño year and a non-El Niño year for our test dataset, and the remaining points as our training dataset."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Pwq1e_IbYRoO"
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "dtNMJqi9YU1l"
},
"source": [
"**Source:** [NOAA \"What is Enso?\"](https://www.climate.gov/enso)\n",
"\n",
"**Caption:** Can we predict whether we are in an El Niño phase based on June temperatures and pressures in Guayaquil, Ecuador?"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"cellView": "form",
"id": "sSkdSpL9rFh8"
},
"outputs": [],
"source": [
"#@title Run this cell to set up the `test` and `train` year lists\n",
"# Let's make our train and test datasets\n",
"def test_train_split(df, rnd_gen):\n",
" nino_years = df.loc[df['El Niño']==1].index.values\n",
" not_nino_years = df.loc[df['El Niño']==0].index.values\n",
"\n",
" nino_idxs = rnd_gen.permutation(np.arange(0,nino_years.size))\n",
" not_nino_idxs = rnd_gen.permutation(np.arange(0,not_nino_years.size))\n",
"\n",
" train = ( list(nino_years[nino_idxs[:-1]]) +\n",
" list(not_nino_years[not_nino_idxs[:-1]]) )\n",
" \n",
" test = [nino_years[nino_idxs[-1]], not_nino_years[not_nino_idxs[-1]]]\n",
" \n",
" return (np.array(test), np.array(train))\n",
"\n",
"# Use test_train_split to make the testing and training datasets\n",
"test, train = test_train_split(A3_df, rnd_gen)\n",
"print(f'Test years: {test}\\n'\n",
" f'Train years: {train}')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "iIlhTA13wTY0"
},
"source": [
"We're going to train a logistic regression classifier on the dataset, but in this exercise we'll rely on the scikit learn implementation!\n",
"\n",
"## **Q4) Make the training and test datasets from the source data.**\n",
"\n",
"Hint 1: Scikit-learn's `LogisticRegression` classifier is documented [at this link](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html).\n",
"\n",
"Hint 2: Before training, use the dataframes' [`.loc` method](https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.loc.html) with the test/train list, then convert the values to numpy (e.g., using [this method](https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.to_numpy.html)) and [`.ravel()`](https://numpy.org/doc/stable/reference/generated/numpy.ravel.html) the truth if necessary. You can also do what was done in the previous section when handling single columns (i.e., using `.values.reshape()` on single column data). "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"cellView": "form",
"id": "mqipa-lv3GNF"
},
"outputs": [],
"source": [
"#@title Let's print out the dataframe head to remember the header columns...\n",
"A3_df.head(5)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "fKh_s6hoaIXP"
},
"outputs": [],
"source": [
"# Get the training and testing dataframes\n",
"train_df = A3_df._______[_______]\n",
"test_df = A3_df._______[_______]\n",
"\n",
"# Extract the training inputs (X_train) and labels (y_train) from \n",
"# the training dataframe\n",
"X_train = _______[['_______','_______']]._______\n",
"y_train = _______[['_______']]._______()._______()\n",
"\n",
"# Do the same with the testing dataframe\n",
"X_test = _______[['_______','_______']]._______\n",
"y_test = _______[['_______']]._______()._______()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "xJYfdKQ3yGCX"
},
"source": [
"## **Q5) Import and instantiate the logistic regression classifier from scikit. Fit it using the training dataset.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "Oc_xk7fcqqF4"
},
"outputs": [],
"source": [
"# Import the LogisticRegression class from sklearn\n",
"from _______._______ import _______\n",
"\n",
"# And instantiate the model\n",
"log_reg = _______()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "z95Vova3wcEJ"
},
"outputs": [],
"source": [
"# Fit the logistic regression to the training set\n",
"log_reg._______(_______, _______)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "cPUIuMA72-6S"
},
"source": [
"That should hopefully have felt much simpler than our previous exercise. Now that you have a trained model, let's see if our model is able to predict whether the test years are El Niño years!\n",
"\n",
"## **Q6) Predict whether each of the two test years was an El Niño year using the logistic regression model, and print out the prediction alongside the truth.**\n",
"\n",
"Hint: To find which method of your `LogisticRegression` classifier to use to make predictions, don't hesitate to consult its documentation [at this link](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "MNCUDNEO30eB"
},
"outputs": [],
"source": [
"# Make predictions using our model!\n",
"prediction = log_reg._______(_______)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "tkcjeHwX2ejf"
},
"outputs": [],
"source": [
"print(f'Was {test[0]} an El Niño year? {bool(y_test[0])}. We predicted {bool(prediction[0])}')\n",
"print(f'Was {test[1]} an El Niño year? {bool(y_test[1])}. We predicted {bool(prediction[1])}')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "TetPoU3M4DV1"
},
"source": [
"If your code reproduces our exact results, you should get the following as a printout: \\\n",
"\n",
"`Was 1951 an El Niño year? True. We predicted True`\\\n",
"`Was 1958 an El Niño year? False. We predicted False`"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "-0cxeKtM4OJM"
},
"source": [
"And with that, we're done for the week! Take a moment to relax, or if you're feeling up to a challenge go back and do the challenge questions for the other notebooks 😀"
]
}
],
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