ClimateMarkov.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Climate Markov Modelling\n",
    "Predict temperature change with Markov probability model.\n",
    "Very good at multi-step predictions.\n",
    "\n",
    "This model has the following assumptions:\n",
    " - Past temperatures in the same time of the year change alike.\n",
    " - All places change alike.\n",
    " - Temperature change is only dependent on the time of the year and the\n",
    "      previous few temperature.\n",
    "\n",
    "Global TODO:\n",
    " - Add support for hemisphere detection (currently all dataset input should\n",
    "   be in the same hemisphere).\n",
    " - Add warping for location of the station. (Hence it's recommended to use\n",
    "   only one location for training.).\n",
    " - Add support for inexact temperature match.\n",
    " - Add time warping.\n",
    " - Return the confidence of the prediction."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "source": [
    "import pickle\n",
    "from typing import BinaryIO, Dict, List, Tuple, Union\n",
    "\n",
    "import gsod\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "from numpy.typing import NDArray\n",
    "from scipy.stats import norm\n",
    "\n",
    "gsod.enable_svg_graphing()"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now let's build a simple first degree Markov predictor."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "source": [
    "class SimpleTemperaturePredict:\n",
    "    \"\"\"Predict temperatures with Markov methods.\"\"\"\n",
    "\n",
    "    def __init__(self):\n",
    "        # Format: {(old_temperature, date_from_jan1): [diff, idx_this]}\n",
    "        # idx_this is for updating average\n",
    "        self._prab: Dict[Tuple[int, int], List[Union[float, int]]] = {}\n",
    "        # Approx. a month around\n",
    "        self._sigma = 10\n",
    "\n",
    "    def _serialize(self):\n",
    "        \"\"\"Serialize data. Responsible for keeping ABI.\"\"\"\n",
    "        return {\n",
    "            \"sigma\": self._sigma,\n",
    "            \"data\": self._prab\n",
    "        }\n",
    "\n",
    "    def _deserialize(self, payload: Dict):\n",
    "        \"\"\"Deserialize into self.\"\"\"\n",
    "        if \"sigma\" in payload:\n",
    "            self._sigma = payload[\"sigma\"]\n",
    "        if \"data\" in payload:\n",
    "            self._prab = payload[\"data\"]\n",
    "            \n",
    "    def save(self, file: BinaryIO):\n",
    "        \"\"\"Save internal dataset.\"\"\"\n",
    "        pickle.dump(self._serialize(), file)\n",
    "\n",
    "    def load(self, file: BinaryIO):\n",
    "        \"\"\"Save internal dataset.\"\"\"\n",
    "        self._deserialize(pickle.load(file))\n",
    "\n",
    "    @staticmethod\n",
    "    def date_to_diff(date: np.datetime64) -> int:\n",
    "        \"\"\"Date to count from Jan 1st.\"\"\"\n",
    "        time_diff = date - date.astype(\"datetime64[Y]\")\n",
    "        return time_diff.astype(\"timedelta64[D]\").astype(int)\n",
    "        \n",
    "    \n",
    "    def fit(self, temperature: NDArray[np.floating], date: NDArray[np.datetime64]):\n",
    "        \"\"\"Fill the internal dataset.\n",
    "\n",
    "        `temperature`: An array of temperature data in chronological order.\n",
    "        `date`: Corresponding dates with the same dimension.\n",
    "        \"\"\"\n",
    "        # Remove the last point because it does not have a next\n",
    "        for (n, t), d in zip(enumerate(temperature), date[:-1]):\n",
    "            tmp_diff = temperature[n+1] - t\n",
    "            old_t = (round(t), self.date_to_diff(d))\n",
    "            if old_t in self._prab:\n",
    "                old_idx = self._prab[old_t][1]\n",
    "                self._prab[old_t][1] += 1\n",
    "                # Average update\n",
    "                self._prab[old_t][0] *= old_idx\n",
    "                self._prab[old_t][0] += tmp_diff\n",
    "                self._prab[old_t][0] /= old_idx + 1\n",
    "            else:\n",
    "                # Initialize\n",
    "                self._prab[old_t] = [tmp_diff, 1]\n",
    "\n",
    "    def predict(self, today_temperature: float, date: np.datetime64, sigma: float = -1):\n",
    "        \"\"\"Predict a temperature change for the tomorrow.\n",
    "\n",
    "        `today_temperature`: Temperature on the day before.\n",
    "        `date`: Date representation of `today_temperature`.\n",
    "        `sigma`: Gaussian stdev.\n",
    "\n",
    "        Return: Temperature difference.\n",
    "        \"\"\"\n",
    "        sigma = sigma if sigma >= 0 else self._sigma\n",
    "        results = []\n",
    "        weights = []\n",
    "        for key in self._prab:\n",
    "            if int(today_temperature) in key:\n",
    "                # XXX: Find KNN here instead of exact match\n",
    "                results.append(self._prab[key][0])\n",
    "                weights.append(norm(self.date_to_diff(date), sigma).pdf(key[1]))\n",
    "        # TODO: Calculate confidence level\n",
    "        return np.average(results, weights=weights)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Specification for datasets."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "source": [
    "STATION = \"722860\"\n",
    "ds = gsod.GsodDataset(\"runtime/GSOD\")\n",
    "temperatures = ds.read_continuous(stn=STATION, year=\"????\", interpolate=True)[\"TEMP\"]"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "source": [
    "# Restrict range for LOOCV\n",
    "load_range = slice(np.datetime64(\"2019-12-31\"))\n",
    "t = temperatures[load_range]\n",
    "dates = t.index.to_numpy()\n",
    "# Train the model\n",
    "model = SimpleTemperaturePredict()\n",
    "model.fit(temperature=t, date=dates)\n",
    "print(model.predict(84.4, np.datetime64(\"2021-07-27\")))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "-0.9923808557514856\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "def next_tmp(model, initial_tmp: float, initial_date: np.datetime64):\n",
    "    prev = initial_tmp\n",
    "    date = initial_date\n",
    "    while True:\n",
    "        prev += model.predict(prev, date)\n",
    "        date += 1\n",
    "        yield prev"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "source": [
    "jan1 = np.datetime64(\"2020-01-01\")\n",
    "count = np.datetime64(\"2020-12-31\") - jan1\n",
    "\n",
    "t = ds.read_continuous(stn=STATION, year=\"2020\", interpolate=True)[\"TEMP\"]\n",
    "d = t.index.to_numpy()\n",
    "\n",
    "plt.plot(d, t, label=\"Real\")\n",
    "\n",
    "# Predict\n",
    "gen = next_tmp(model, t[jan1], jan1)\n",
    "itms = np.fromiter(gen, float, count=count.astype(int))\n",
    "plt.plot(jan1 + np.arange(count).astype(\"timedelta64[D]\"), itms, label=\"Prediction\")\n",
    "\n",
    "# Chart data\n",
    "plt.xlabel(\"Date\")\n",
    "plt.ylabel(\"Temperature/${}^\\circ$F\")\n",
    "plt.title(f\"LOOCV Predicted and Real Temperature for 2020 - Station {STATION}\")\n",
    "plt.legend()"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x14e093b20>"
      ]
     },
     "metadata": {},
     "execution_count": 6
    },
    {
     "output_type": "display_data",
     "data": {
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  {
   "cell_type": "markdown",
   "source": [
    "What is the error of this model?"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "rmse = np.average(((t[1:] - itms) ** 2) ** 0.5)\n",
    "rmse"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "4.4664919157102885"
      ]
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "metadata": {}
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