Lab 6 Time Series.ipynb

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 "cells": [
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    "## Lab 6: Time Series Analysis\n",
    "\n",
    "**Purpose** : The purpose of this lab is to establish a foundation for time series analysis of remotely sensed data, usually in the form of a temporally ordered stack of images.  You will be introduced to concepts of smoothing, interpolation, linear modeling and phenology.  At the completion of the lab, you will be able to perform analysis of multi-temporal data for determining trend and seasonality on a per-pixel basis.\n",
    "\n",
    "**Prerequisites** : Lab 5\n",
    "\n",
    "### 1. Multi-temporal data in Earth Engine\n",
    "\n",
    "Time series in Earth Engine are represented as image collections.  This can make time series analysis complicated because\n",
    "\n",
    "- There is a different time series in each pixel\n",
    "- The size (length) of the time series vary across pixels\n",
    "- Missing data may occur in any pixel at any time (e.g. due to cloud masking)\n",
    "\n",
    "As a result of these complicating factors, analyzing time series in Earth Engine is unlike traditional methods.  Specifically, use joins to define temporal relationships between collection items.  As you will soon discover, it's possible to perform many traditional time series methods by mapping functions over joined collections.\n",
    "\n",
    "First, some very basic notation.  A scalar pixel at time *t* is given by $p_{t}$ and a pixel vector by $P_{t}$.  An estimate is a variable with a hat on: e.g. the estimated pixel value at time is $p̂_{t}$.  A time series is just a collection of *N* pixels, sorted chronologically: ${ P_{t}; t = t_{0}...t_{N}}$, where *t* might be in any units, $t_{0}$ is the smallest and $t_{N}$ is the largest such *t* in the series.\n",
    "\n",
    "### 2. Data preparation and preprocessing\n",
    "\n",
    "The first step in analysis of time series data is to import data of interest and plot it at an interesting location.\n",
    "\n",
    "a. **Load a time series of Landsat data**\n",
    "\n",
    "- Search for Landsat 8 surface reflectance and import the &quot;USGS Landsat 8 Surface Reflectance Tier 1&quot; collection.  Name it l8sr.\n",
    "\n",
    "- Make a single point geometry with the geometry drawing tools and position the point in a location of interest.  (How about an annual grassland or a deciduous forest?)  Name the import roi.\n",
    "\n",
    "b. **Filtering, masking and preparing bands of interest**\n",
    "\n",
    "- preprocess the Landsat imagery by filtering it to the location of interest, masking clouds, and adding the variables in the model:"
   ]
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   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true,
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   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'geetools'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_84/3405973428.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mgeemap\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;31m# import geetools for cloud /sadow discrimination\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mgeetools\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mui\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcloud_mask\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0mMap\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgeemap\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mMap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# from ipygee\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'geetools'"
     ]
    }
   ],
   "source": [
    "import ee\n",
    "ee.Initialize()\n",
    "\n",
    "import geemap\n",
    "# import geetools for cloud /sadow discrimination\n",
    "from geetools import ui, cloud_mask\n",
    "\n",
    "Map = geemap.Map()  # from ipygee\n",
    "Map"
   ]
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  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
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   "outputs": [],
   "source": [
    "import datetime\n",
    "from matplotlib import dates\n",
    "import matplotlib.dates as mdates\n",
    "from pylab import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "l8sr = ee.ImageCollection(\"LANDSAT/LC08/C01/T1_SR\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "roi = ee.Geometry.Point([-122.977389, 38.753458])\n",
    "Map.addLayer(roi, {'outline_color': 'red'}, name='Region of Interest - ROI')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# // This field contains UNIX time in milliseconds.\n",
    "timeField = 'system:time_start';"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "using Landsat BQA layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# CLOUD MASKING IN EE PYTHON NOT QUITE EASY. USING THE GEETOOLS custom functions https://github.com/gee-community/gee_tools \n",
    "\n",
    "# this function only for Landsat 8 Surface Corrected single image\n",
    "mask_l8SR_all = cloud_mask.landsatSR() #this function masks clouds, snow, shadows\n",
    "\n",
    "# mask_l8SR_cloud = cloud_mask.landsatSR(['cloud'])\n",
    "# mask_l8SR_shadow = cloud_mask.landsatSR(['shadow'])\n",
    "# mask_l8SR_snow = cloud_mask.landsatSR(['snow'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating a function for masking the entire ImmageCollection\n",
    "def maskL8sr(image):\n",
    "    cld_free=mask_l8SR_all(image)\n",
    "    return cld_free"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# // Use this function to add variables for NDVI, time and a constant\n",
    "# // to Landsat 8 imagery.\n",
    "def addVariables(image):\n",
    "    #   // Compute time in fractional years since the epoch.\n",
    "    date = ee.Date(image.get(timeField))\n",
    "    years = date.difference(ee.Date('1970-01-01'), 'year')\n",
    "    #   // Return the image with the added bands.\n",
    "    return image.\\\n",
    "    addBands(image.normalizedDifference(['B5', 'B4']).rename('NDVI')).\\\n",
    "    addBands(ee.Image(years).rename('t')).\\\n",
    "    float().\\\n",
    "    addBands(ee.Image.constant(1))\n",
    "\n",
    "\n",
    "# // Remove clouds, add variables and filter to the area of interest.\n",
    "filteredLandsat = l8sr.\\\n",
    "  filterBounds(roi).\\\n",
    "  map(maskL8sr).\\\n",
    "  map(addVariables)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c. **Plot the time series at the location of interest**\n",
    "\n",
    "- To visualize the data, make a chart at the location of interest.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "info = filteredLandsat.getRegion(roi,30).getInfo()# 30 is Landsat resolution\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We separate the information returned into column headers and data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['id', 'longitude', 'latitude', 'time', 'B1', 'B2', 'B3', 'B4', 'B5', 'B6', 'B7', 'B10', 'B11', 'sr_aerosol', 'pixel_qa', 'radsat_qa', 'NDVI', 't', 'constant']\n"
     ]
    }
   ],
   "source": [
    "# extract the header column names\n",
    "print(info[0])\n",
    "header = info[0]\n",
    "# create a Numpy array of the data\n",
    "data = array(info[1:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we extract time information and convert it to at Python datatime data type."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# extract the time information\n",
    "iTime = header.index('time')\n",
    "# convert to Python datetime objects\n",
    "time = [datetime.datetime.fromtimestamp(i/1000) for i in (data[0:,iTime].astype(int))]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract the data columns what we want to display on the plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "xBand = 'time'\n",
    "yBandList = [\n",
    "        'NDVI',\n",
    "        u'B10' #B10 is a thermal band in Landsat\n",
    "        ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "iBands = [header.index(b) for b in yBandList]\n",
    "yData = data[0:,iBands].astype(np.float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 960x640 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# matplotlib date format object\n",
    "\n",
    "fig = figure(figsize=(12, 8), dpi=80)\n",
    "\n",
    "# plot the band values\n",
    "ax1 = fig.add_subplot(211)\n",
    "ax1.plot(time,\n",
    "         yData[:, -1] * 0.1 - 273.15,\n",
    "         'o',\n",
    "         color=\"red\",\n",
    "         label=\"Temperature Celsius\")\n",
    "# ax1.plot(time, yData[:,3], 'o', color=\"magenta\",  label=\"Band 4\")\n",
    "ax1.legend(loc='best')\n",
    "ax1.grid(True)\n",
    "\n",
    "#plt.title('Band values as a function of time')\n",
    "ax1.set_ylabel('Temperature Celsius')\n",
    "\n",
    "# plot NDVI\n",
    "ax2 = fig.add_subplot(212, sharex=ax1)\n",
    "ax2.plot(time, yData[:, 0], 'o', color=\"black\", label=\"NDVI\")\n",
    "ax2.legend(loc='best')\n",
    "ax2.grid(True)\n",
    "start, end = ax2.get_xlim()\n",
    "ax2.xaxis.set_ticks(np.arange(start, end, 64.5))\n",
    "\n",
    "# Format the ticks.\n",
    "years = mdates.YearLocator()  # every year\n",
    "months = mdates.MonthLocator()  # every month\n",
    "yearsFmt = mdates.DateFormatter('%Y')\n",
    "\n",
    "ax2.set_ylabel('NDVI')\n",
    "\n",
    "ax2.xaxis.set_major_locator(years)\n",
    "ax2.xaxis.set_major_formatter(yearsFmt)\n",
    "ax2.xaxis.set_minor_locator(months)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Linear modeling of time\n",
    "Lots of interesting analyses can be done to time series by harnessing the linearRegression() reducer.  For example,\n",
    "\n",
    "a. **Estimate linear trend over time\n",
    "\n",
    "Consider the following linear model, where et is a random error:\n",
    "\n",
    "pt = β0 + β1t + et\t\t\t(1)\n",
    "\n",
    "This is the model behind the trendline added to the chart you just created.  This model is useful for detrending data and reducing stationarity in the time series (Shumway and Stoffer 2017).  For now, the goal is to discover the values of the β's in each pixel.\n",
    "\n",
    "To fit this trend model to the Landsat-based NDVI series using ordinary least squares (see Lab 5), use the linearRegression() reducer:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# // List of the independent variable names\n",
    "independents = ee.List(['constant', 't'])\n",
    "\n",
    "# // Name of the dependent variable.\n",
    "dependent = ee.String('NDVI')\n",
    "\n",
    "# // Compute a linear trend.  This will have two bands: 'residuals' and\n",
    "# // a 2x1 band called coefficients (columns are for dependent variables).\n",
    "trend = filteredLandsat.select(independents.add(dependent)).\\\n",
    "    reduce(ee.Reducer.linearRegression(independents.length(), 1))\n",
    "\n",
    "Map.addLayer(trend, {}, 'trend array image')\n",
    "Map.centerObject(roi.buffer(1000))  #centering the map to landsat scene\n",
    "\n",
    "# // Flatten the coefficients into a 2-band image\n",
    "coefficients = trend.select('coefficients').\\\n",
    "  arrayProject([0]).\\\n",
    "  arrayFlatten([independents])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coefficients image is a two band image in which each pixel contains values for β0 and β1.   \n",
    "\n",
    "- Use the model to \"detrend\" the original NDVI time series:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# // Compute a de-trended series.\n",
    "\n",
    "\n",
    "def detrend(image):\n",
    "    return image.select(dependent).subtract(\n",
    "          image.select(independents).multiply(coefficients).reduce('sum')).\\\n",
    "          rename(dependent).\\\n",
    "          copyProperties(image, [timeField])\n",
    "\n",
    "\n",
    "detrended = filteredLandsat.map(detrend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "info = detrended.getRegion(roi,30).getInfo()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We separate the information returned into column headers and data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['id', 'longitude', 'latitude', 'time', 'NDVI']\n"
     ]
    }
   ],
   "source": [
    "# extract the header column names\n",
    "print(info[0])\n",
    "header = info[0]\n",
    "# create a Numpy array of the data\n",
    "data = array(info[1:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we extract time information and convert it to at Python datatime data type."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# extract the time information\n",
    "iTime = header.index('time')\n",
    "# convert to Python datetime objects\n",
    "time = [datetime.datetime.fromtimestamp(i/1000) for i in (data[0:,iTime].astype(int))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "xBand = 'time'\n",
    "yBandList = [\n",
    "        'NDVI'\n",
    "        ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "iBands = [header.index(b) for b in yBandList]\n",
    "yData = data[0:, iBands].astype(np.float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0NEx4/Ki38E+mpTjIqZjz3clcvHgx3/ve93ImieqKObFS7lClE76wroFRmrykUmXJTOqnTJm4GhT160alROUOrkhaJJIUM1tsZs+YWY+Zfc/MXptjm/lm9m0z+5mZ/SCMcopI9WTeWdmyZQuzZs1idHSUoaGh8cr7kSNH+PCHP8x3vvMd2tvbi+oqFuUW/lJbiqvRFSffncx58+apK+Yk5btDlS0KCV+UJi8pVJaBgQF6enoumiUtV2U7M6nfsWNHwRnr0qJ+3aiEsNadEikkKgPn/wF4yN23m9lNwOeAN2Vt83NgA/Bq4CNVLp+IhCDdegxw+vTpvJX348ePjw/4P3ToEPfddx8nTpyouckWSl2DpVrrCOVbK6IW1k6I0qxUabkmX7hw4cL4APmmpqbIrG4epclLCk2wMTIywtatW3nggQfGn0vHMd/6SsWohetGufJN5FCvM/VJdIR+J8XMpgOvB76YemonsMDM5mdu5+4vuXs3cK66JRSRsBXTzaNQV7FaaeEvtdU6Cl1xotwVM8qtw9l3qJ566inOnz/PU089Famxd1GavCS7LC0tLeOvuTtnz55laGho/Cf7zmK+9ZXSmpqaxn/PtGnTaua6Ua4ojTsSyRSFOym/Cpxw92EAd3czOwa0AX1hFkxEoqHUynsttPDnUmqrdZS64kRNLbQOFztlcdiKOZ+qdccqsyy7du3igQcemHBNmWLWV5o6dSq33HILt912G1Bf66SUegdXpFqikKQAZHecLuuKYGbrgHXpxy0tLXR1dZV8nIGBgUntJ8VTjMe+3Pfv38+JEyeYPXs2y5Ytq+iXYjVjHNR7cXemT5/OyZMnGRkZGX++oaGBGTNmcPbs2bzvcdasWZw7d44nn3yy7HLkU8kY33vvvaxfv55Tp06RSCQYHh5m1qxZ3HvvvZe8h3LiUotKifO+ffs4cuRIztbh3t5eNm/ezFVXXRVEMWvaRDHOdT6dPn36ks/szJkz2bRpEzNmzAisrBcuXKChoaGohS+nTJnCkSNHGBgYyPn60NAQHR0d49MQB3ndiNr33pkzZ/LGZWBggDNnzkSqvMWKWpzjKPAYu3uoP8B04GdAIvXYgFPA/Dzb/zbwg1J+x5w5c3wynnjiiUntJ8Wr9xj39fX5kiVLPJlMemtrqyeTSV+yZIn39fVV7HdUK8ZBv5dcx1+6dKn39/dX5PjlqHSMR0dHfc+ePb5t2zbfs2ePj46O5t02ynGptFLivG3bNm9tbXXGGsEu+mltbfVt27YFV9AaVmyM05/RRx55xNva2jyRSFwU40Qi4UuXLi342S3Xnj17PJlM5vwbZ/8kk0l/+umnfcmSJaGUNVPUvvdGR0cjEZdKi1qc46jcGAPHvUD9PfQ7Ke7+gpn9EHg3sB24Eehz974wyyUSNK+B7ijFqsZ7qdUuXJORb6B6LlGLi0dkoHqhrnDnz5/nlVdewd1j+fkJWuYq7Q0NDTlnyKr05A25FBpInyndXXLFihWXTFgQlQkKwpRrIgfFRaIg9CQl5f3AdjO7l7FZvG4DMLN/BL7h7t8wsybgMNAEvNrMjgNfcPe/DKvQIuWo1sxM2YKoRIY9y1S9i0pcMiuv6YpOemalefPmVbUshSqwo6Oj/Nmf/RlbtmwJpWyVEFYymN0gUUjQ4xmKnSVtwYIFbNy4kUcffZT29nYOHDjAM888E3oiHSVRa+wQgYgkKe7+HJdOOYy7/1HG/y8Ac6tZLqlf1agAhDFYMahKpAZeSlh3BvOdq5kV2PTYFE+tl+HuF836VEt3LSHcZLCYVdrTqjF5Q67K9bXXXjuehLS2trJhwwZuueWWS2Kla9LFSm3siMpd08kotey1/F5rWSSSFJEoqVYFoNozMwVZidQsUxLGncGJztV0Bfazn/0sH/jAB6p+1zIIYXcTLdQgkama64vkmyVt+fLldHR0xKJLbdRE6a5pqUotey2/11oX+jopIlGSWQEIagXvtHyrTgf15R7kXPj53ktDQwMzZ87k0KFDl6z8LPFS7TVbij1X02teNDc3V61sQarUeezueVdlL6RQgwSMTeUblfVFtP5HMKr5PVlppZa9lt9rHChJEclQzS+1ai+SFmQlMtd7aWxspKGhgZMnT7J27dpILaQnlVftu2mlnKtxutNXifO4nEUuCzVItLW18elPfzoyC1FGYbHTOKrl5K/Ustfye40DJSkiGQp9qTU0NJTc6jiR7FWng/xyD7qilvletmzZwqxZsxgdHc258rNan+Kn2ncGS6mAVrtsQSr3PC63ZThf48rixYvZs2cP733ve1mxYkUkulHFKTmNklpO/kotey2/1zhQkiKSYaJpS3fs2FHxOwLp/tSrV68O9Mu9GhW19HtZvHgxp0+fVutTHan2ncFSKqDVLluQJnsep7t3rV+/Pu8il0eOHGH//v0TlqGajSvliFNyGiWFzr2BgQF6enoi27231MRViW64lKSIZMj3pZZ2/vz5su8ITLYveLmqWVFT61N9qmbltdQKaK1UrCcymfM4s3vX5s2b867QnkwmOXHiRNHlmGzjSrWugXFKTqOk0PfkyMgIW7dujWz33lKvG0p0w6XZvUQyZM+7X+mFysKeJaRac+Gr9al+VWvNlsksQBeV9WTKVcp5XMq6JoODg8yePTuoYgPVvwZq/Y/Kyz73GhsbOXfuHDD2eTt79iwQzVnUSr1uaKHLcClJEcmS+aW2fft2duzYkTNRKbT+R6451YFIrDBfjYpavoX01PoklVRuBbSW1z4o9jwudl2T9Lm5bNmyShbzImFNnxyX5DRKMs+9Xbt28cADD1xyh254eJje3l7Wr1/PW9/61sicX6VeN5TohkdJikgO6S81gC984Qs5t8l3RyBfS+HGjRtDWWE+DGp9kmqZbAU07Lua1TLRuiZNTU24+/i5efDgwcDKEsZaOhKc9LnX29tLU1NTzm6Ew8PDbN68mU984hMXnV9hNxCUet1QohsOjUkRKaDU/qiFZs5Zs2ZNXY3TiMsYAImfelr7oFDXy0Qiwbp166p2bmqsWjxNtHbOhQsXLjq/+vr6Jj0FttQX3UkRKaDYOwLpVqFdu3blnTnnJz/5Sd6WoriO01Drk2QLuwUV6qtFv1DXy/b2djZt2lS1+GusWjzl+4xlGx4e5vDhw1x//fWcOHEi1G7PUhuUpIhQuOI0UX/UzG4jZpZ35pympiYuu+wyfvKTn2ichtSlqHSxKtQFqtBYs1oUpa6XGqsWT9mfMTPL270wkUiMJyiZ4thAIOVTkiJ1r5iKU747AqXMnDM0NMTWrVvZsGFD6JUFkWoLa9B0LvXWoh+Vgb9RSpiksooZSA9j51cymcz5fRm3BgIpn5IUqWvlVpxKnTnnxhtv5MYbbwy9siBSbVHqYlWPLfpR6XoZlYRJKi/9GVu+fDlf+9rXcp5fs2fP5tSpUzn3j2MDgZRHA+elrhVTcSqk0EBQGOvilb14WLVWmBeJkigNmtYif+HSNbB4YS3+W45C59fTTz+txRGlaLqTInWt3L7pxcycc8MNNwDw1FNPqdVQ6lbUulhVokU/CpMA1IN6jXNUxnBNRqHzS13+pFiRSFLMbDHwKPArwP8FVrv7gRzb3Q7cw9gdoN3AXe5euJ+NSAHlVpwmmjnnT/7kT1i1alVNfsmIVFIUu1iV0wWqliuQtaRe4xylMVyTle/8imKXv3pNhKMuKt29/gF4yN2vBP4W+Fz2Bma2APgYsAJoB2YCt1ezkBI/pa6Dkq3Qbe0nnniCVatW1cVaDCITiVMXq3paZyVM9RzncrsiR12Uuvz19/dr3ZaICj1JMbPpwOuBL6ae2gksMLP5WZveBHzd3U/72JXpQeDmqhVUYqkSFad8ixb++Mc/DuVLphb7MEt9iMsCn3GvQEZFPcc5SmO44qyeE+FaEIXuXr8KnEh323J3N7NjQBvQl7FdG5CZ1valnruEma0D1qUft7S00NXVVXLBBgYGJrWfFC8qMf7kJz/J/v37OXHiBLNnz2bZsmUcPHiQgwcPlnScWbNmce7cOZ588kmefPLJvEnOlClT+PrXv865c+cuec3dLylLsa1Mp0+fZv369Zw6dYpEIsHw8DAzZszgb/7mb5gxY0ZJ70WKF5XPcS3JPFeKFZU4T/bcrgVRiTHEN87FxPjMmTMMDAzk3f/MmTOR+TtFVTFx3rdvX94FmHt7e9m8eTNXXXVVkMWsaYFfL9w91B/gN4D9Wc99H7gu67mtwP+T8XgZcKSY3zFnzhyfjCeeeGJS+0nx4hzjPXv2eDKZdOCSn2Qy6Xv27Llkn76+Pl+yZIknk0lvbW31ZDLpS5Ys8b6+vgl/3+joqC9ZssQTicRFv6uhocGXLl3qo6OjQbxN8Xh/jqMkKnGezLldK6ISY/f4xrmYGOe7nicSCV3Pi1RMnLdt2+atra05P2Otra2+bdu24Ataw8q9XgDHvUD9PfTuXsCPgblmlgCwsWaTXwWOZW13DJif8Xhejm1EIqPU8S5e5m3nfF0jRkZGYt81QqSayh3LJsWp5zjHaQxXlEVt1kG5WOhJiru/APwQeHfqqRuBPnfvy9p0J/D7ZjYjlcjcAfxT1QoqUqJSv2SCXLNFfZhFKkcVyOqo9zjHZQxXlE0mEfYKj/ss93jZ+4+OjsZmXGoUxqQAvB/Ybmb3Aj8HbgMws38EvuHu33D3I2b218BexpKrp8gxC5hIlJQy1WKQa7aoRUikfJ41TemBAwd45plnNG1pgKI4XW01lTNNtkys1HVbJjMldvZ1I/PzW+4U29n7Z9Yfmpqaan7K7kgkKe7+HPCmHM//Udbjh4GHq1UukUoo9kumUJIxMDBAT08P3d3deb+g861DMWXKFGbOnMmhQ4fGt6uXL/hMhb4oRCZSqDKhCmSwVFGXIBWbCGd2yS527ZpC1422tray1sLJV560oaGhko4XRaF39xKRMfluO8PYuJKtW7cWnL89V9eIxsZGpkyZwsmTJ1m7dm3dzv+uefClHOWOFxNJc3f27dsXi644pap0N6lKKmbdllK7ZE903eju7i6ri3e+8mSr5Sm7laSIRER2ktHS0jL+mrsXVTHK7MO8ZcsWZs2ahbszNDRUtxUrVTClXPW8XodUTrqx5J577qm7xpI4NBSVOu5zouvG448/XtY40kLlmczxokhJikiEZCYZa9euzXkBmqhilG4RWrx4MadPn2ZkZKSk/eMmjhXMKLdIxpEmpZByZXfNqafGkrg0FJU67nOi60Z6v2KPV0p5JnO8KFKSIhIx6STjyiuvpKmpKec25bay1FPFKm5xiEOLZK3RpBRSrjg2lhQrLu+91JnAJrpu3HDDDWVNsV2oi/hkjhdFSlJEIqrcipEqVmPiFIe4tEjWmnper0MqI4zGkqjccY1LQ1GpU2JPdN1YsWJFzuMtWrSIjRs38uijjxb8u+Ubh5pMJmlsbIzFlN2RmN1LRC6Vb7auUltZent7L+ryVW8Vq3LjGCXFtEhqBqTKK3WaUpFs1W4sKXdq20qKU0NRKVNiF3PdyD5ea2srGzZs4JZbbinq75arPNdee21spkZXkiJ1qRamoy23YpTef8WKFbzwwgt1W7GKUwWz3LV0alHmuXrmzBne8pa3hPI3q/f1OqQ81WwsmcxUuUGKU0MRlDYldjHXjfTxli9fTkdHR8l/t1zlicuU3UpSpO5EqYVpIuVWjObNm8fDDz9Ma2trIBWrWkj2ID4VzDi1SBYj+1wdGBjg4YcfDu1c1XodMlmZjSWHDx+mubk5sMaSqN1xjVND0WQUe92I2t8tCpSkSF2JWgtTMcqtGAVVsaqlZA/iUcGMW4tkIbV4rkr8ldMwk24s2bx5M5dffnlgjSVRvOMal4aiIEXx7xY2JSlSV9RSURmqQIajnlokda5K1FSiYcbMuOqqq+js7AysnFG94xqHhqIgFfq7DQwM0NPTQ3d3d10ld5rdS+pKXGYZCVtcppSsRZlr6WzdupXdu3dz4MAB2trawi5aRelclSippZn1NBtdtOWbda3QlMIjIyNs3bq17qacV5IidSWqLUy1Jg4VyImm54zK9J25pFskV69ezYoVK2LZqqZzVaKklhpmSp0qV6qn0DpX2X+3lpaW8f3cPdKJcVDU3UvqSj316Q9SrVcgc3XbmD9/Pps2beLs2bPj00DWynibONK5KlFSa+MFNAYkeorpJp35d9u1axcPPPAAQ0NDFx2nnrq8KkmRcbUyU1M56qlPf5BquQKZ74uip6eHd77znUybNo1z586Nb6/xNuHIda4ODAyoNVhCUYsNMxoDEi3FjrNL/916e3tpamq6JEmBaCbGQVCSUscyk5J6ajlWC1P5ajnZy/dFAWPnRGaCkqmeWq+iIvtcPXPmDOvWrYv050viqZYbZiQaSr0bV4uJcaWFnqSY2TTgc8A1wChwj7t/Lc+2XwWuBWYBl7n72aoVNGYyu7s0NjbWXcuxWpjKV6vJXqEviomE1XpVD3c588k8V6OeAEt81XLDjERDqUmHEuMIJCnAh4AL7t5uZguA75jZt9z9pzm2fRC4Czhd1RLGTL7uLtnUciwTqcVkr9AXxUTCaL2qtfVoROKqVhtmJBpKTTqUGEcjSXkXsBrA3Y+a2dPA24Ht2Ru6+zeBuvjDVEp2C+y1117Lgw8+eMlJkk+99HuU+pHvi2IiYbReaT0akWipxYYZiYbJJB31nhhHIUlpAzInfO5LPRcb5XTVKGff7BbYdPeW0dFRRkZGijpGZstxPXc5kfjI/qLI7u6YvW1LS0torVda0FDqgb5bpF5MJumo58TYgp5n2cz2AB15Xr4aOAAsdPcXU9vfD7zs7h8tcEynwJgUM1sHrEs/bmlpmbNz586Syz4wMEBzc3PJ+2U6ffo069ev59SpUyQSCYaHh5k5cyabNm1ixowZuDv79+/nxIkTzJ49m2XLlo1/WCfatxB354//+I85efJk0QlJtoaGBmbPns1DDz3ECy+8MOmyFFKJGEthinFumedec3Mzn//85y/5fN92222cP3/+knMzW1AxfvLJJ/nMZz7DwMDAJa81Nzdz11138Za3vKXivzeq9FkOXrVjXM73XK3S57g6FOfglRvjVatWPe/uc/Nu4O6h/gD7gWsyHn8FWD3BPg60Fvs75syZ45PxxBNPTGq/tNHRUV+yZIknEglPldkBTyQSvnTpUj969KgvWbLEk8mkt7a2ejKZ9CVLlnhfX9+E+46Ojub9nXv27PG//Mu/9MbGxov2LebHzMbLsnTpUu/v7590WYpRboxlYopxcdLnzrZt23zPnj0lfa6DivGePXs8mUzmPFeTyaTv2bMnkN8bVdX+LJfzmahV1YxxkN8tUaZrcnUozsErN8bAcS9Qf49Cd6/HgLuB1amB89cDd4RbpMoo1FXj8OHDXH/99Zw4cSJnX/OHHnqo5G4emd27zCzn3Nr5JBIJFi1axKZNm3j55ZcvugXZ3d2tLicSe1G8pa7ZXcKjCQuCp+6MEhR3Z9++fZw8eVJdCGtYFJKU+4FHzKyXsSmI73b3lwDM7A5gtrt/OPX4G8DrU/s9Z2aH3P23QyhzUQpNdZpIJMYTlEzpi/Pjjz9e0nzanjXAthQNDQ38/d//PXfeeWfOk7jWVtoViQvN7hKO7OupJiwIhr5bJAjpBobDhw/T3NysBoYaFnqS4u7nGJvhK9drD2Y9/r2qFKpCJpoTO5lM5kwoksnk+Db59s2eBrXQAnWFJBIJ2tvb8yYooAWFRMJU77O7hEEt/NWh7xaptOwGhrNnx4Yuq4GhNk0JuwBxlu6qkUhcnAsmEgnmzJmTd0D74OAgN9xwQ959c3XzSLdI5dPU1ERjYyPJZJLGxkZaW1tJJpO0t7dP2CJb6H2oy4lI8NJd0VavXs2KFSv0JRsQd6e7u5vt27czZUrur8d0C7+UT98tUmnFNDBI7VCSEqB0V41FixaRTCYvSgyefvrpghfn9OrKufbNlVQUapFKJBKsW7eOp556ivPnz/PUU0+xdetWdu/ezYEDB2hrKzzjc6H3oS4n9SWzEtfd3Z2eyEKk5vX399PR0cHKlSvZsWMH58+fz7mdWvgrJ47fLbpGhqtQg60aGGpP6N294q5QV42J+pqX0s2j0ADb9vZ2Nm3aNL7fZAYHq8uJaCCxxFWxY/rUwl95cfpu0TUyfOpCGC8TJilmdleh1939M5UrTjzlmzWomItzsTMOVWOAbXZZ0i1Gtf7FIhPTQGKJs4nG9E2dOpWRkRFNWBCQKM6sVypdI6NBMyLGSzF3Uq4p8JruY5apkhfnarZIqcWovmggscRZoVmmpk6dyi233MLq1avVECN56RpZHnevSN0ls8E2c3YvNTDUpmKSlD9299KmjJLQVKNFSi1G9UdThUqcFeoiMjIyMj5hgUg+ukZOXqUbPdMNtps3b+byyy9XT48aVszA+RNmdr+ZdQReGqkJmj2j/qifr8SZZpmScukaOTmZjZ6Dg4OcPXuWwcHB8UbPyU48YGZcddVVmhGxxhWTpHQCzcAeM3vGzG43s9aAyyURVqnZM9IrwmoWlOhTJU7iLI6zTEl16Ro5OWr0lEIm7O7l7j8E1pjZnwPvAN4LfMLMdgKfc/dnAi6jREwlWoy0Imxt0crnEndxmmVKqk/XyMlRNzkppOgpiN19EPgn4J/MbBHwZWAP0BBQ2SSiyp09QyvC1iZV4iTu4jDLlISnGtfISg0wjwp1k5NCSlonxcxeB7wPuAXoAf4oiEJJtJXbYqRZUGqXKnEi0RS3ymutCvIaGcdZNeMwZbDOveAUs07KLzGWlNwOzAK+APyWuz8XcNkkwsppMdLtXRGRyolj5VUuFtdZNWu9m5zOvWAVcyflx8BTwEeBf9Z0xJI22RajQrd3BwYG6Onpobu7W60RIiITiGvltVZUqxU9zj0QarUrsc694BUzu9did/89YDfw62b2Bs3uJeXINwsKjK1JsHXrVlauXElHRwf9/f0hlFBEpDZodqTw9Pf309HRwcqVK1mzZk2g31uVmlUzqtKNnrU0ZbDOveAVk6ScMrNPAmeAb6Z+zpjZ31ktfIokcjKn+0wkErS0tIy/5u4VmyddRCTu4l55jaqg1vfIRwPMo0fnXvCKSVL+FPgNYJm7v8bdXwO8DnhD6jWRkqVv73784x9n7dq1OU90tUaIiBSmyms4qt2KrnVYokfnXvCKSVLeDfyhux9KP5EaNH9r6rWymNk0M/uymfWaWY+ZvSPPdrPNrMvMnjOzfzezr5jZL5f7+yU86RVhr7zySpqamnJuo9YIEZH8VHkNR7Vb0bXgaPTo3AteMUnKq939WPaT7t4HvLoCZfgQcMHd2xlb3f4zqRnFso0AH3P3Je7+OqAf+HgFfr+ETK0RIiKTo8prOML43kr3QNi9ezdbt25l9+7dHDhwgLa2tor/LpmYzr3gFTO717lJvlasdwGrAdz9qJk9Dbwd2J65kbufBk5nPPWvwB0V+P0SsjjMky4iEpZanR2ploX1vaW1qqJF516wbKLBXWZ2Gng010vAre4+s6wCmL0MLHL3F1KP/xY46+4fLbBPA2MD+P+Xu/99jtfXAevSj1taWubs3Lmz5LINDAzQ3Nxc8n5SvHSMT58+zfr16zl16hSJRILh4WFmzZrFpk2bmD59etjFrGn6HAdPMa4OxTl4inHxJvu9pRhXh+IcvHJjvGrVqufdfW6+14tJUv660Ovu/pEJ9t8DdOR5+WrgALDQ3V9MbX8/8HK+JCU1o9iDwHTgRncfLfgGgLlz5/rx48cn2uwS6QWGpDJyzSf/5JNPjsdYq7YGQ5/j4CnG1aE4B08xLs1kvrcU4+pQnINXbozNrGCSUkx3r29N+rcD7v5bhV43s2PAfODF1FPzgF0FdtkC/Crw34pJUKKiHirghd5jvlVZ77333vH9dRtbRERqib63RIJTTJLyCcAZ696V5sBsYBbQUGYZHgPuBlab2QLgevKMNTGzLUA7YwlK7hFrEZSvgt7V1cW8efPCLl5FFHqPbW1teVdl3bBhA7feemvsEjYREZEoqYfGUomXCWf3cvdr3P03U/9ew9gMXN1AEijYFaxI9wNTzawX6ALudveXAMzsDjP7aOr/y4E1jN11+Vcze9bMvl6B3x+oai/4FIaJ3mN3d3fe+eRPnjypdVBEREQC1N/fT0dHBytXrmTNmjWsXLmSjo4O+vv7wy6aSF7F3EkBwMyagT8DPgh8GXitu/+k3AK4+znGZvjK9dqDGf/fy8V3c2pCMQs+1fpt4one4+OPP05jYyMXLly4ZN9EIkFvb2/Nx0BERCSKMhsSs3szrFq1igMHDuiOikTShHdSzGyKmf0JcAhYBrzR3T9YiQSlHlR7wacwTPQegbzzyQ8PD2sdFBERkYAU01gqEkXFLOa4D/gfwF8Cf8NY16zXpn8CLV0M1MNChYXe48DAAO7OzJkzc67KOmvWLK2DIiIiEpB6aCyVeCqmu9c0xgbKf4zcA+gXBlCu2KiHhQrzvUeAkZERPvWpT3HhwgXMjMbGRpqamhgcHGThwoXce++9us0sIiISkHpoLJV4Kmbg/Hx3X5D6WZjx/wXurgRlAmZGV1cXixYtIplM0traSjKZpL29na6urlhU0LPfY0tLy/hr7s7Zs2cZGhpidHSUWbNmsWXLFnbv3s2BAwe0UKOIiEiA0g2JuXozxKWxVOKpmO5eUqZ58+Zx8OBBdu/ezdatW8cr6G1tbWEXrWIy3+PatWtz3loeGRnh1KlTLF68mBUrVsQiQRMREYmyemgslXgqenYvKU89LPiUfo+9vb00NTUxNDR0yTbp/q9xjoOIiEiUpBsStU6K1BIlKVJx6v8qIiISLbXUWKqFJwWUpEgA6mGyABEREam8/v5+Ojs7OXr0KMlkksHBQebPn8+mTZs4e/askpY6oiRFKi7d/zX7IrNw4UL1fxUREZGc8i082dPTwzvf+U5aWloYHBxkwYIFdHV1MW/evJBLLEFSkiKBUP9XERERKUW+hSfhF7OFAhw+fJhVq1Zx4MAB1StiTEmKBKaW+r+KiIhIuNILT164cKHgdsPDwxw5coS9e/eqjhFjmoJYREREREJXaOKdbOnZQiW+lKSIiIiISOjyLTyZi2YLnZi7093dzfbt2+nu7sbdwy5SSdTdS0RERERClz3xTmNjI+fOnbtkO80WOrE4zJKmJEVEREREIiF74p3W1lY2bNig2UJLEJdZ0kJPUsxsGvA54BpgFLjH3b+WY7sW4CmgOfXUSeAOd++rUlFFREREJGDZE+/ceOONmi20BHGZJS30JAX4EHDB3dvNbAHwHTP7lrv/NGu788DvuvvLAGb2QWAz8I6qllZEREREqkazhZYmLrOkRWHg/LuATwO4+1HgaeDt2Ru5+2hGgmLAqxi78yIiIiIiIsRnlrQoJCltQH/G477UczmZ2TeBU8A7gbWBlkxEREREpIbEZZY0C3o6MjPbA3Tkeflq4ACw0N1fTG1/P/Cyu3+0wDGnAOuBWe5+V47X1wHr0o9bWlrm7Ny5s+SyDwwM0NzcPPGGMmmKcfAU4+ApxtWhOAdPMQ6eYlwd9R7n06dPs379ek6dOkVDQ0POrl8NDQ3Mnj2bhx56aFJjUsqN8apVq55397n5Xg88SZmIme0HVrv791OPvwLscvftE+w3Ezjk7pdN9Dvmzp3rx48fL7ls6WnwJDiKcfAU4+ApxtWhOAdPMQ6eYlwdivPYIPliZklra8vbgamgcmNsZgWTlCgMnH8MuBtYnRo4fz1wR/ZGZjYDGHL3l1JP/Xfg36tWShERERGRGlHrs6RFIUm5H3jEzHoZGwh/dzoRMbM7gNnu/mFgLvCwmSUAAw4D7w6pzCIiIiIiNaPWZkkLPUlx93OMzfCV67UHM/7/b8Drq1UuEREREREJRxRm9xIRERERERmnJEVERERERCJFSYqIiIiIiESKkhQREREREYkUJSkiIiIiIhIpSlJERERERCRSlKSIiIiIiEikKEkREREREZFIUZIiIiIiIiKRoiRFREREREQiRUmKiIiIiIhEipIUERERERGJFCUpIiIiIiISKUpSREREREQkUpSkiIiIiIhIpChJERERERGRSAk9STGzaWb2ZTPrNbMeM3tHEfs8YmZuZq3VKKOIiIiIiFRPIuwCAB8CLrh7u5ktAL5jZt9y95/m2tjM/ivgVS2hiIiIiIhUTeh3UoB3AZ8GcPejwNPA23NtaGaXA38NrKta6UREREREpKrMPdybEmb2MrDI3V9IPf5b4Ky7fzTHtv8EfNHd/9nMHLjM3c/m2G4dGYlMS0vLnJ07d5ZctoGBAZqbm0veT4qnGAdPMQ6eYlwdinPwFOPgKcbVoTgHr9wYr1q16nl3n5vv9cC7e5nZHqAjz8tXp/7NzJQsz3H+ABh093+e6He6+2Zgc/rx3LlzvbOzs7gCZ+jq6mIy+0nxFOPgKcbBU4yrQ3EOnmIcPMW4OhTn4AUd48CTFHf/rUKvm9kxYD7wYuqpecCuHJu+GfgdM+vLeG6/mb3N3f+jAkUVEREREZEIiMKYlMeAuwFSA+evB76RvZG73+Xuc919vrvPTz29TAmKiIiIiEi8RCFJuR+Yama9QBdwt7u/BGBmd5jZJWNTREREREQkvkKfgtjdzzE2w1eu1x4ssF/OsSsiIiIiIlLbonAnRUREREREZJySFBERERERiRQlKSIiIiIiEilKUkREREREJFKUpIiIiIiISKQoSRERERERkUhRkiIiIiIiIpGiJEVERERERCJFSYqIiIiIiESKkhQREREREYkUJSkiIiIiIhIpSlJERERERCRSlKSIiIiIiEikKEkREREREZFIUZIiIiIiIiKREnqSYmbTzOzLZtZrZj1m9o4C27qZ/buZPZv6+a1qllVERERERIKXCLsAwIeAC+7ebmYLgO+Y2bfc/ad5tr/W3c9WsXwiIiIiIlJFod9JAd4FfBrA3Y8CTwNvD7VEIiIiIiISmigkKW1Af8bjvtRz+XzbzH5kZpvNrCXQkomIiIiISNWZuwf7C8z2AB15Xr4aOAAsdPcXU9vfD7zs7h/Ncaw2dz+WSk4eTG13V47t1gHr0o9bWlrm7Ny5s+SyDwwM0NzcXPJ+UjzFOHiKcfAU4+pQnIOnGAdPMa4OxTl45cZ41apVz7v73HyvB56kTMTM9gOr3f37qcdfAXa5+/YJ9nsT8JC7/6eJfsfcuXP9+PHjJZetq6uLzs7OkveT4inGwVOMg6cYV4fiHDzFOHiKcXUozsErN8ZmVjBJiUJ3r8eAuwFSA+evB76RvZGZ/ZKZTUv9fwpjY1l+WMVyioiIiIhIFUQhSbkfmGpmvUAXcLe7vwRgZneYWbrb11Lgu2b2I+A/gMuBD4ZQXhERERERCVDoUxC7+znG7orkeu3BjP9/B3hdtcolIiIiIiLhiMKdFBERERERkXFKUkREREREJFKUpIiIiIiISKQoSRERERERkUhRkiIiIiIiIpGiJEVERERERCJFSYqIiIiIiESKkhQREREREYkUJSkiIiIiIhIpSlJERERERCRSEmEXQERERCrL3dm7dy+9vb20t7ezfPlyzCzsYomIFE1JioiISIz09/fT2dnJ0aNHSSaTDA4OsmDBArq6upg3b17YxRMRKYq6e4mIiMSEu9PZ2cnhw4cZHBzk7NmzDA4OcvjwYVatWoW7h11EEZGiKEkRERGJib1799LX18fw8PBFzw8PD3PkyBH27t0bUslEREqjJEVERCQment7aWxszPlaMpmkt7e3yiUSEZkcJSkiIiIx0d7ezuDgYM7XBgcHaW9vr3KJREQmJ/QkxcymmdmXzazXzHrM7B0Ftv0lM/uSmR0ys4Nm9vFqllVERCTKli9fzoIFC0gkLp4XJ5FIsHDhQpYvXx5SyUREShN6kgJ8CLjg7u1AJ/AZM/ulPNs+AvzQ3Re7ewfw99UqpIiISNSZGV1dXSxatIhkMklrayvJZJL29na6uro0DbGI1IwoTEH8LmA1gLsfNbOngbcD2zM3MrN24PXAjenn3P1k1UopIiJSA+bNm8fBgwe1ToqI1DQLezpCM3sZWOTuL6Qe/y1w1t0/mrXd7wF/ARwA3gD8BPgf7v7DHMdcB6xLP25paZmzc+fOkss2MDBAc3NzyftJ8RTj4CnGwVOMq0NxDp5iHDzFuDoU5+CVG+NVq1Y97+5z870e+J0UM9sDdOR5+erUv5mZUr6mnkbgTcBfufufmFkn8L/NbL67XzTXortvBjanH8+dO9c7OztLLntXVxeT2U+KpxgHTzEOnmJcHYpz8BTj4CnG1aE4By/oGAeepLj7bxV63cyOAfOBF1NPzQN25di0H3je3b+VOm6XmSWBuUBfpcorIiIiIiLhisLA+ceAuwHMbAFwPfCNHNv9G/BzM3tdats3pJ5/vhqFFBERERGR6ojCwPn7gUfMrBcYBe5295cAzOwOYLa7f9jd3cxWA/9oZs3AAHCjuw+FVXAREREREam80AfOV4OZXeAX3ckyTQXOF9i1FTib57VC+0503MnuG9Rxw9w3ajGO476FYlzO743iey3n2FGMcS3uG9b1otD+UYxTVPcN43oR1nGDPHatXS+iGKdy91X9Ivh9y/0st7p7U9693b1uf4CvTPD68cnsW8RxJ7VvUMcNed9IxTim++aNcTm/N4rvNcQyBxLjWtw3rOtFof2jGKcI71v160VYxw2xzJG7XkQxThXYV/WL4PcN7LPs7pEYkxKmxwLad6LjTnbfoI4b5r5BHVf7Fi+Iz2OY7zWMMk8kirGKYhzLiXGh/aMYp6juO5GofS7Cul6Uu29Qx43a3yfMfYM6rvYtXll/v7ro7jVZZnbcC8zfLOVTjIOnGAdPMa4OxTl4inHwFOPqUJyDF3SM6/1OykQ2T7yJlEkxDp5iHDzFuDoU5+ApxsFTjKtDcQ5eoDHWnRQREREREYkU3UkREREREZFIUZIiIiIiIiKRUhdJipk1m9n/MrMeM3vWzJ4ws/mp16anHh8ys31mtiJjv/eZ2X+Y2bCZ/WnWMe9OvfZs6t+1VX5bkRJEjDO2WWJmr5jZA1V6O5EV0Gf5PjN7IXW8Z83sS1V+W5ES1GfZzG5Mvb7fzA6kj1mvAvosb8n4HD9rZgP1fG0OKMaXp47572Z20MweNbOpVX5rkRFQjGeY2ddSMf7/zOyD1X1X0VJGjP8m9Rn9kZl9z8x+J+O1KWa21cwOm1mvmd0VwluLlIDi/F/M7AdmdsEmU4ebaI7iOPwAzcBb+cUYnD8Fnkz9/xHgvtT/rwH6gUTq8a8BHcDngT/NOuarM/7/KuAY8Lqw32ucYpx6vQH4NrADeCDs9xn2T0Cf5fsU28BjfDVwEJidevwqYFrY7zVucc46/kzGFhGbGfZ7jVOMgb8DNqf+3wA8AdwV9nuNWYy/BHwk9f9W4N+Ba8J+rzUY4xuAqRnx/inQnHr8HmB36jP8y0AfsDTs9xrDOF+Zem4jk6hn1MWdFHcfcPddnooY8F1gYer/7wQ+ndru+8BpYEXq8Y/c/SAwmuOYP8t4OA1IAHU7C0EQMU65B/hnoCeosteSAOMsKQHF+M+BT7j7idS2P3f3VwJ8G5FXhc/ye4Audz9V8cLXiABjfJmZTQGSjH3/HQ/oLUReQDH+NeD/TW13FvgX4NbA3kTElRHjx909vdr5fzCWkPxK6vG7gAfdfcTdXwK+Avz3wN9MhAURZ3fvcfcfAcOTKVNdJCk5rAX+t5ldDkxx9xczXusD2oo5iJndZGb7Gcso73f3/6h4SWtX2TE2s9cBnYy13EluFfksAzenbtU+ZWZvrnQha1wlYvxaoM3M/sXMfmhmHzOzhgDKWssq9VlOex/wuQqVLS4qEeOPAe3AKeAF4KC7f6PSBa1hlYjx94FbUl2SpjP2PTi/0gWtYZOJ8XuBw+6eTqjbGKu7TbRfPatEnMtSd0mKmd0LLAbWp57KvvthxR7L3b/q7suAJcB7zGxJZUpZ2yoRYzNrBB4G7nD3kcqWMB4q+Fl+EJjv7r8G/BXwP81sXmVKWdsqGONG4DeAVcBy4E3A+ytRxjio5HU5dbzljHWp21V+6eKhgjH+A8a6H80CZgNXmtnqSpSx1lUwxn/O2Of3/zDWHewpYKgSZax1k4mxma0E/ppL75Rk7lvSNSbuKhznSaurJMXMPgS8A7jB3V9x9zOp56/I2GweY+NLiubufcC/Am+rUFFrVgVjPAtYBOwysz7gg8Afm5laRqnsZ9ndT7n7UOr/e4EfAm+ofKlrS4WvF/3ATnc/n+rm9TXgNytd5loU0HX5duBRNXCMqXCM1wBfSnWTeRn4KlD3d18rfE1+yd3f5+6/7u6rUk8fqHiha8xkYmxm1wPbgP/q7s9lbHeMi+9OlVz3i6sKx7ksdZOkmNk64GbgP7v7/8146THg7tQ21zA22LK7iON1ZPz/CmAlY61LdauSMXb3Y+7+K+4+393nA58EHnb32wMoek0J4LM8N+P/i4FfZ6xfad2qdIwZm/jhLanuGw3AfwZ+VNFC16AA4oyZtQI3MTbQs+4FEOMjjA2UTd/xXgXsq2CRa04A1+TLU7HFzF4P/DfgM5UtdW2ZTIzN7DrgC8DbU+MiyNrv/WbWYGa/zNgYlf8Z6JuoAQHEuTwegRkFgv4B5jJ2q+ow8Gzq519Tr80AngQOAfuB6zP2ezdjAwLPMTZbwXHg6tRrn0lt/yxjlY26nd0kqBhnHf8+NANVUJ/lRxmrZDwL/BtwU9jvM4YxngJsZmyGr32p60dj2O81bnFOvX478C9hv78o/AT0WV4AdKU+xwcY65bbFPZ7jVmMbwB6U9eL7wHXhf0+azTGhxgb4P1sxs9/Sr3WwNhA8MOpn7wzBdbLT0Bx/u3UZ/vnwMup//9esWVKTzMmIiIiIiISCXXT3UtERERERGqDkhQREREREYkUJSkiIiIiIhIpSlJERERERCRSlKSIiIiIiEikKEkREREREZFIUZIiIiIiIiKRoiRFREREREQiRUmKiIiIiIhEyv8PfagptlkPh7AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 960x640 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# // Plot the detrended results.\n",
    "# var detrendedChart = ui.Chart.image.series(detrended, roi, null, 30)\n",
    "#     .setOptions({\n",
    "#       title: 'Detrended Landsat time series at ROI',\n",
    "#       lineWidth: 1,\n",
    "#       pointSize: 3,\n",
    "#     });\n",
    "# print(detrendedChart);\n",
    "\n",
    "fig = figure(figsize=(12, 8), dpi=80)\n",
    "\n",
    "# plot detrended\n",
    "ax2 = fig.add_subplot(211)\n",
    "ax2.plot(time, yData[:, 0], 'o', color=\"black\", label=\"NDVI\")\n",
    "ax2.legend(loc='best')\n",
    "ax2.grid(True)\n",
    "start, end = ax2.get_xlim()\n",
    "ax2.xaxis.set_ticks(np.arange(start, end, 64.5))\n",
    "\n",
    "# Format the ticks.\n",
    "years = mdates.YearLocator()  # every year\n",
    "months = mdates.MonthLocator()  # every month\n",
    "yearsFmt = mdates.DateFormatter('%Y')\n",
    "\n",
    "ax2.set_ylabel('NDVI')\n",
    "\n",
    "ax2.xaxis.set_major_locator(years)\n",
    "ax2.xaxis.set_major_formatter(yearsFmt)\n",
    "ax2.xaxis.set_minor_locator(months)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### d. Estimate seasonality with a harmonic model\n",
    "\n",
    "Consider the following linear model, where et is a random error, A is amplitude, ω is frequency, and φ is phase:\n",
    "\n",
    "pt = β0 + β1t + Acos(2πωt - φ) + et \n",
    "\n",
    "    = β0 + β1t + β2cos(2πωt) + β3sin(2πωt) + et\t\t(2)\n",
    "\n",
    "Note that β2 = Acos(φ) and β3 = Asin(φ), implying A = (β22 + β32)½ and φ = atan(β3/β2).  (See Shumway and Stoffer (2017) equations 4.1 - 4.2).  To fit this model to the time series, set ω=1 (one cycle per unit time) and use ordinary least squares regression.\n",
    "\n",
    "- The setup for fitting the model is to first add the harmonic variables (the third and fourth terms of equation 2) to the image collection.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# // Use these independent variables in the harmonic regression.\n",
    "harmonicIndependents = ee.List(['constant', 't', 'cos', 'sin'])\n",
    "\n",
    "\n",
    "# // Add harmonic terms as new image bands.\n",
    "def harmonic_terms(image):\n",
    "    timeRadians = image.select('t').multiply(2 * 3.1416)\n",
    "    return image.\\\n",
    "    addBands(timeRadians.cos().rename('cos')).\\\n",
    "    addBands(timeRadians.sin().rename('sin'))\n",
    "\n",
    "\n",
    "harmonicLandsat = filteredLandsat.map(harmonic_terms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Fit the model as with the linear trend, using the linearRegression() reducer:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "harmonicTrend = harmonicLandsat.\\\n",
    "  select(harmonicIndependents.add(dependent)).\\\n",
    "  reduce(ee.Reducer.linearRegression(\n",
    "    numX= harmonicIndependents.length(),\n",
    "    numY= 1\n",
    "))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Plug the coefficients in to equation 2 in order to get a time series of fitted values:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# // Turn the array image into a multi-band image of coefficients.\n",
    "harmonicTrendCoefficients = harmonicTrend.select('coefficients').\\\n",
    "  arrayProject([0]).\\\n",
    "  arrayFlatten([harmonicIndependents])\n",
    "\n",
    "\n",
    "# // Compute fitted values.\n",
    "def fitting_harm(image):\n",
    "    return image.addBands(\n",
    "    image.select(harmonicIndependents).\\\n",
    "      multiply(harmonicTrendCoefficients).\\\n",
    "      reduce('sum').\\\n",
    "      rename('fitted'))\n",
    "\n",
    "\n",
    "fittedHarmonic = harmonicLandsat.map(fitting_harm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "info = fittedHarmonic.getRegion(roi,30).getInfo()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We separate the information returned into column headers and data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['id', 'longitude', 'latitude', 'time', 'B1', 'B2', 'B3', 'B4', 'B5', 'B6', 'B7', 'B10', 'B11', 'sr_aerosol', 'pixel_qa', 'radsat_qa', 'NDVI', 't', 'constant', 'cos', 'sin', 'fitted']\n"
     ]
    }
   ],
   "source": [
    "# extract the header column names\n",
    "print(info[0])\n",
    "header = info[0]\n",
    "# create a Numpy array of the data\n",
    "data = array(info[1:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we extract time information and convert it to at Python datatime data type."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# extract the time information\n",
    "iTime = header.index('time')\n",
    "# convert to Python datetime objects\n",
    "time = [datetime.datetime.fromtimestamp(i/1000) for i in (data[0:,iTime].astype(int))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "xBand = 'time'\n",
    "yBandList = [\n",
    "        'NDVI',\n",
    "        'fitted'\n",
    "        ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "iBands = [header.index(b) for b in yBandList]\n",
    "yData = data[0:,iBands].astype(np.float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 960x640 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# // Plot the detrended results.\n",
    "# var detrendedChart = ui.Chart.image.series(detrended, roi, null, 30)\n",
    "#     .setOptions({\n",
    "#       title: 'Detrended Landsat time series at ROI',\n",
    "#       lineWidth: 1,\n",
    "#       pointSize: 3,\n",
    "#     });\n",
    "# print(detrendedChart);\n",
    "\n",
    "fig = figure(figsize=(12,8), dpi=80)\n",
    "\n",
    "# plot detrended\n",
    "ax2 = fig.add_subplot(211)\n",
    "ax2.plot(time, yData[:,-2], 'o', color=\"red\", label=\"NDVI\")\n",
    "ax2.plot(time, yData[:,-1], 'o', color=\"blue\",  label=\"Harmonic Fitting\")\n",
    "ax2.legend(loc='best')\n",
    "ax2.grid(True)\n",
    "start, end = ax2.get_xlim()\n",
    "ax2.xaxis.set_ticks(np.arange(start, end, 64.5))\n",
    "\n",
    "# Format the ticks.\n",
    "years    = mdates.YearLocator()   # every year\n",
    "months   = mdates.MonthLocator()  # every month\n",
    "yearsFmt = mdates.DateFormatter('%Y')\n",
    "\n",
    "ax2.set_ylabel('NDVI')\n",
    "\n",
    "ax2.xaxis.set_major_locator(years)\n",
    "ax2.xaxis.set_major_formatter(yearsFmt)\n",
    "ax2.xaxis.set_minor_locator(months)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Although any coefficients can be mapped directly, it is useful and interesting to map the phase and amplitude of the estimated harmonic model.  First, compute phase and amplitude from the coefficients, then map:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "# // Compute phase and amplitude.\n",
    "phase = harmonicTrendCoefficients.select('sin').\\\n",
    "    atan2(harmonicTrendCoefficients.select('cos')).\\\n",
    "    unitScale(-3.1416, 3.1416);\n",
    "    \n",
    "amplitude = harmonicTrendCoefficients.select('sin').\\\n",
    "    hypot(harmonicTrendCoefficients.select('cos')).\\\n",
    "    multiply(5);#     // Add a scale factor for visualization.\n",
    "\n",
    "# // Compute the mean NDVI.\n",
    "meanNdvi= filteredLandsat.select('NDVI').mean();\n",
    "\n",
    "# // Use the HSV to RGB transform to display phase and amplitude.\n",
    "rgb = ee.Image.cat([\n",
    "  phase,      #// hue\n",
    "  amplitude,  #// saturation (difference from white)\n",
    "  meanNdvi    #// value (difference from black)\n",
    "]).hsvToRgb();\n",
    "\n",
    "Map.addLayer(rgb, {}, 'phase (hue), amplitude (sat), ndvi (val');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- More on harmonic models\n",
    "\n",
    "It's worth noting that a time series can be decomposed as the sum of sinusoids at different frequencies (See Shumway and Stoffer (2017), equation 4.7).  The harmonic model presented here can be easily extended in this manner by adding bands that represent higher frequencies (e.g. timeRadians.multiply(2).cos().rename('cos2') and the corresponding sin() band for a harmonic component with two cycles per year) and amending the harmonicIndependents variable accordingly.  If you're feeling plucky, check out this implementation of that idea for an arbitrary number of harmonic terms.  While this will undoubtedly improve the goodness-of-fit of the model, many of the coefficients may be close zero.  To estimate the importance of terms representing seasonality or higher-frequency harmonic behavior (e.g. double-cropping), an F-statistic can be used when the model assumptions are satisfied.  See for example, Shumway and Stoffer (2017), equation 2.11.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Autocovariance and autocorrelation\n",
    "The autocovariance of a time series refers to the dependence (specifically the covariance) of values in the time series at time t with values at time h = t − l, where l is the lag.  The autocorrelation is the covariance normalized by the standard deviations of the covariates.  Specifically, assume our time series is stationary and define the autocovariance and autocorrelation according to Shumway and Stoffer (2017) equations 1.27 and 1.26, respectively.  Comparing values at time t to previous values is useful not only for computing autocovariance, but also for a variety of other time series analyses as well, as you'll see shortly.  \n",
    "\n",
    "To combine image data with previous values, in Earth Engine, the first step is to join the previous values to the current values.  To do that, use a join to create what we'll call a lagged collection:\n",
    "\n",
    "a. **Create a lagged ImageCollection**\n",
    "\n",
    "Consider the following function to create a lagged collection:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lag(leftCollection, rightCollection, lagDays):\n",
    "    filter = ee.Filter.And(ee.Filter.maxDifference(\n",
    "      difference= 1000 * 60 * 60 * 24 * lagDays,\n",
    "      leftField= timeField, \n",
    "      rightField= timeField\n",
    "    ), \n",
    "    ee.Filter.greaterThan(\n",
    "      leftField= timeField, \n",
    "      rightField= timeField\n",
    "  ))\n",
    "    return ee.Join.saveAll(\n",
    "    matchesKey= 'images',\n",
    "    measureKey= 'delta_t',\n",
    "    ordering= timeField, \n",
    "    ascending= False).apply(\n",
    "    primary= leftCollection, \n",
    "    secondary= rightCollection, \n",
    "    condition=filter\n",
    "  )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function joins a collection to itself, using a filter that gets all the images before but within a specified time difference (in days) of each image.  That list of previous images within the lag time is stored in a property of the image called images, sorted reverse chronologically.  For example, to create a lagged collection from the detrended Landsat imagery:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "lagged17 = lag(detrended, detrended, 17);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Why 17 days?  Recall that the temporal cadence of Landsat is 16 days.  Specifying 17 days in the join gets one previous image, but no more.  To compute autocovariance or other interesting statistics, map functions over the lagged collection as in the following sections.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b. **Compute autocovariance and autocorrelation**\n",
    "\n",
    "- The autocovariance reducer expects a set of one-dimensional arrays as input.  So pixel values corresponding to time t need to be stacked with pixel values at time t − l as multiple bands in the same image.  Consider the the following function for that purpose:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def merger(current, previous):\n",
    "    return ee.Image(previous).addBands(current)\n",
    "\n",
    "\n",
    "def merge(image):\n",
    "#   // Function to be passed to iterate.\n",
    "    return ee.ImageCollection.fromImages(image.get('images')).iterate(merger, image);\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\t\t...and use that function to merge the bands from the lagged collection:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "merged17 = ee.ImageCollection(lagged17.map(merge));\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Now the bands from time t and h are all in the same image.  Note that the band name of ph was the same as pt.  During the merging process, it gets a '_1' appended to it.  Use a function to convert the merged bands to arrays with bands pt and ph, then reduce with the covariance reducer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def imarray(image):\n",
    "    return image.toArray();\n",
    "\n",
    "\n",
    "def covariance(mergedCollection, band, lagBand):\n",
    "    return mergedCollection.select([band, lagBand]).map(imarray).reduce(ee.Reducer.covariance(), 8);\n",
    "\n",
    "\n",
    "lagBand = dependent.cat('_1');\n",
    "covariance17 = ee.Image(covariance(merged17, dependent, lagBand))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The output of the covariance reducer is an array image, in which each pixel stores a 2x2 variance-covariance array.  The off diagonal elements are covariance, which you can map directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Map.addLayer(covariance17.arrayGet([0, 1]), {'max': 0.1,'min':-0.1,'palette':['white', 'blue']}, 'covariance (lag=17 days)');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The diagonal elements of the variance-covariance array are variances.  Use this function to compute correlation from the variance-covariance array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def correlation(vcArrayImage):\n",
    "    covariance = ee.Image(vcArrayImage).arrayGet([0, 1]);\n",
    "    sd0 = ee.Image(vcArrayImage).arrayGet([0, 0]).sqrt();\n",
    "    sd1 = ee.Image(vcArrayImage).arrayGet([1, 1]).sqrt();\n",
    "    return covariance.divide(sd0).divide(sd1).rename('correlation')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\t\t...and map the correlation:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "correlation17 = correlation(covariance17);\n",
    "Map.addLayer(correlation17, {min: -1, max: 1,'palette':['blue','white', 'red']}, 'correlation (lag = 17 days)');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's worth noting that you can do this for longer lags as well (try 34 days) in Cell 34.  Of course, that images list will fill up with all the images that are within l of t.  Those other images are also useful, for example in fitting autoregressive models as described later."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5 Cross-covariance and Cross-correlation\n",
    "\n",
    "Cross-covariance is analogous to auto-covariance, except instead of measuring the correspondence between a variable and itself at a lag, it measure the correspondence between a variable and a covariate at a lag.  Specifically, define the cross-covariance and cross-correlation according to Shumway and Stoffer (2017) equations 1.30 and 1.31, respectively.  \n",
    "\n",
    "You already have all the code needed to compute cross-covariance and cross-correlation!  But you do need a time series of another variable.  Suppose we postulate that NDVI is related in some way to the precipitation before the NDVI was observed.  To estimate the strength of this relationship (in every pixel), load precipitation, join, merge, and reduce as previously:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# // Precipitation (covariate)\n",
    "chirps = ee.ImageCollection('UCSB-CHG/CHIRPS/PENTAD');\n",
    "\n",
    "# // Join the t-l (l=1 pentad) precipitation images to the Landsat.\n",
    "lag1PrecipNDVI = lag(filteredLandsat, chirps, 5);\n",
    "\n",
    "# // Add the precipitation images as bands.\n",
    "merged1PrecipNDVI = ee.ImageCollection(lag1PrecipNDVI.map(merge));\n",
    "\n",
    "# // Compute and display cross-covariance.\n",
    "cov1PrecipNDVI = covariance(merged1PrecipNDVI, 'NDVI', 'precipitation');\n",
    "# Map.addLayer(cov1PrecipNDVI.arrayGet([0, 1]), {}, 'NDVI - PRECIP cov (lag = 5)');\n",
    "\n",
    "# // Compute and display cross-correlation.\n",
    "corr1PrecipNDVI = correlation(cov1PrecipNDVI);\n",
    "Map.addLayer(corr1PrecipNDVI, {min: -1, max: 1,'palette':['blue','white', 'red']}, 'NDVI - PRECIP corr (lag = 5)');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What do you observe from this result?  Specifically, how can we do better?  One possible drawback of this computation is that it's only based on five days of precipitation, whichever five days came right before the NDVI image.  Perhaps precipitation in the month before the observed NDVI is relevant?  Test that idea with the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# // Join the precipitation images from the previous month\n",
    "lag30PrecipNDVI = lag(filteredLandsat, chirps, 30);\n",
    "# print(lag30PrecipNDVI.getInfo());\n",
    "\n",
    "def imagesum(image):\n",
    "    laggedImages = ee.ImageCollection.fromImages(image.get('images'));\n",
    "    return ee.Image(image).addBands(laggedImages.sum().rename('sum'));\n",
    "\n",
    "\n",
    "sum30PrecipNDVI = ee.ImageCollection(lag30PrecipNDVI.map(imagesum));\n",
    "\n",
    "# // Compute covariance.\n",
    "cov30PrecipNDVI = covariance(sum30PrecipNDVI, 'NDVI', 'sum');\n",
    "# Map.addLayer(cov1PrecipNDVI.arrayGet([0, 1]), {}, 'NDVI - sum cov (lag = 30)');\n",
    "\n",
    "# // Correlation.\n",
    "corr30PrecipNDVI = correlation(cov30PrecipNDVI);\n",
    "Map.addLayer(corr30PrecipNDVI, {min: -0.5, max: 0.5,'palette':['blue','white', 'red']}, 'NDVI - sum corr (lag = 30)');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe that the only change is to the merge() method.  Instead of merging the bands of the NDVI image and the covariate (precipitation), the entire list of precipitation is summed and added as a band (eliminating the need for iterate()).\n",
    "\n",
    "As long as there is sufficient temporal overlap between the time series, these techniques can be extended to longer lags and longer time series.  But watch out.  There are some nuances to determining the statistical significance of correlation estimates.  See Shumway and Stoffer (2017) example 1.26 for details.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6. Auto-regressive models\n",
    "\n",
    "The discussion of autocovariance preceded this section in order to introduce the concept of lag.  Now that you have a way to get previous values of a variable, it's worth considering auto-regressive models.  Suppose that pixel values at time t depend in some way on previous pixel values.  If you have observed significant, non-zero autocorrelations in a time series, this may not be a crazy assumption.  Specifically, you may postulate a linear model such as:\n",
    "\n",
    "pt = β0 + β1pt-1 + β2pt-2 + et\t\t\t\t\t(3)\n",
    "\n",
    "To fit this model, you need a lagged collection as created previously except with a longer lag (e.g. l = 34 days).  The next steps are to merge the bands, then reduce with the linear regression reducer.\n",
    "\n",
    "- Create a lagged collection, where the images list stores the two previous images:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "lagged34 = ee.ImageCollection(lag(filteredLandsat, filteredLandsat, 34));\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Merge the bands of the lagged collection such that each image has bands at time t and bands at times t-1,..., t − l.  Note that it's necessary to filter out any images that don't have two previous temporal neighbors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def imlist(image):\n",
    "    return image.set('n', ee.List(image.get('images')).length())\n",
    "\n",
    "\n",
    "merged34 = lagged34.map(merge).map(imlist).filter(ee.Filter.gt('n', 1));\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Fit the regression model using the linearRegression() reducer:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "arIndependents = ee.List(['constant', 'NDVI_1', 'NDVI_2']);\n",
    "\n",
    "ar2 = merged34.\\\n",
    "  select(arIndependents.add(dependent)).\\\n",
    "  reduce(ee.Reducer.linearRegression(arIndependents.length(), 1));\n",
    "\n",
    "# // Turn the array image into a multi-band image of coefficients.\n",
    "arCoefficients = ar2.select('coefficients').\\\n",
    "  arrayProject([0]).\\\n",
    "  arrayFlatten([arIndependents]);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Compute the fitted values using an expression.  Because this model is a function of previous pixel values, which may be masked, if any of the inputs to equation 3 are masked, the output of the equation will also be masked.  That's why you should use an expression here, unlike the previous linear models of time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "# // Compute fitted values.\n",
    "def imcoefs(image):\n",
    "    return image.addBands(\n",
    "        image.expression('beta0 + beta1 * p1 + beta2 * p2', {\n",
    "          'p1':image.select('NDVI_1'),\n",
    "          'p2': image.select('NDVI_2'),\n",
    "          'beta0': arCoefficients.select('constant'),\n",
    "          'beta1': arCoefficients.select('NDVI_1'),\n",
    "          'beta2': arCoefficients.select('NDVI_2')\n",
    "            }).rename('fitted'));\n",
    "    \n",
    "fittedAR = merged34.map(imcoefs)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Plot the results.  Note the missing values that result from masked data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "info = fittedAR.getRegion(roi,30).getInfo()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We separate the information returned into column headers and data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['id', 'longitude', 'latitude', 'time', 'B1', 'B2', 'B3', 'B4', 'B5', 'B6', 'B7', 'B10', 'B11', 'sr_aerosol', 'pixel_qa', 'radsat_qa', 'NDVI', 't', 'constant', 'B1_1', 'B2_1', 'B3_1', 'B4_1', 'B5_1', 'B6_1', 'B7_1', 'B10_1', 'B11_1', 'sr_aerosol_1', 'pixel_qa_1', 'radsat_qa_1', 'NDVI_1', 't_1', 'constant_1', 'B1_2', 'B2_2', 'B3_2', 'B4_2', 'B5_2', 'B6_2', 'B7_2', 'B10_2', 'B11_2', 'sr_aerosol_2', 'pixel_qa_2', 'radsat_qa_2', 'NDVI_2', 't_2', 'constant_2', 'fitted']\n"
     ]
    }
   ],
   "source": [
    "# extract the header column names\n",
    "print(info[0])\n",
    "header =info[0]\n",
    "# create a Numpy array of the data\n",
    "data = array(info[1:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we extract time information and convert it to at Python datatime data type."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "# extract the time information\n",
    "iTime = header.index('time')\n",
    "# convert to Python datetime objects\n",
    "time = [datetime.datetime.fromtimestamp(i/1000) for i in (data[0:,iTime].astype(int))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "xBand = 'time'\n",
    "yBandList = [\n",
    "        'NDVI',\n",
    "        'fitted'\n",
    "        ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "iBands = [header.index(b) for b in yBandList]\n",
    "yData = data[0:,iBands].astype(np.float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 960x640 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# // Plot the detrended results.\n",
    "# var detrendedChart = ui.Chart.image.series(detrended, roi, null, 30)\n",
    "#     .setOptions({\n",
    "#       title: 'Detrended Landsat time series at ROI',\n",
    "#       lineWidth: 1,\n",
    "#       pointSize: 3,\n",
    "#     });\n",
    "# print(detrendedChart);\n",
    "\n",
    "fig = figure(figsize=(12,8), dpi=80)\n",
    "\n",
    "# plot detrended\n",
    "ax2 = fig.add_subplot(211)\n",
    "ax2.plot(time, yData[:,-2], 'o', color=\"red\", label=\"NDVI\")\n",
    "ax2.plot(time, yData[:,-1], 'o', color=\"blue\",  label=\"Autoregresive Fitting\")\n",
    "ax2.legend(loc='best')\n",
    "ax2.grid(True)\n",
    "start, end = ax2.get_xlim()\n",
    "ax2.xaxis.set_ticks(np.arange(start, end, 64.5))\n",
    "\n",
    "# Format the ticks.\n",
    "years    = mdates.YearLocator()   # every year\n",
    "months   = mdates.MonthLocator()  # every month\n",
    "yearsFmt = mdates.DateFormatter('%Y')\n",
    "\n",
    "ax2.set_ylabel('NDVI')\n",
    "\n",
    "ax2.xaxis.set_major_locator(years)\n",
    "ax2.xaxis.set_major_formatter(yearsFmt)\n",
    "ax2.xaxis.set_minor_locator(months)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At this stage, note that the missing data has become a real problem.  Any data point for which at least one of the previous points is masked or missing is also masked.  It may be possible to avoid this problem by substituting the output from equation 3 (the modeled value) for the missing or masked data.  Unfortunately, the code to make that happen is not straightforward.  If you're feeling brave, check out [this solution](https://code.earthengine.google.com/c5fbadc5136d94e80ba428376b05d148).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assignment:\n",
    "    \n",
    "Create a notebook, change the location (the roi coordinates in Cell 4) ane evaluate the capability of harmonic and autoregression approaches to estimate NDVI and the relationship between Precipitation and NDVI in one of these sites:\n",
    "\n",
    "a) Desert location (Death Valley in CA), \n",
    "b) The Nile Delta \n",
    "\n",
    "Or you can do two notebooks and see how these different enviroments behave in a time series analysis.\n",
    "\n",
    "Happy Coding\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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