Scale_CLIMdistribution.ipynb

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   "cell_type": "markdown",
   "id": "f76b0c9c-ff7b-49fa-8173-e790ca4b2be0",
   "metadata": {},
   "source": [
    "# Description"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aef35016-bf8f-41ba-9e64-dabf9d7e106e",
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   "source": [
    "This notebook uses the median- and quantile-derived scale factors ($\\beta$ values, outputs from [MedianScaling_calculate_beta.ipynb](./MedianScaling_calculate_beta.ipynb) and [QuantileScaling_calculate_beta.ipynb](./QuantileScaling_calculate_beta.ipynb), respectively) to scale the climatological distribution (CLIM) of maximum temperatures (defined as the collection of observations over 1985-2015) at each location globally and for each month of the year.\n",
    "\n",
    "The resulting forced and counterfactual distributions of maximum temperatures are used in the the observation-based attribution analysis. Example attributuon analyses with these output distributions at Phoenix, AZ, USA, are provided in XXXXXXXX."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b54c357a-2ed8-4344-8f96-05dd2cc6c1d2",
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   "source": [
    "import numpy as np\n",
    "import xarray as xr\n",
    "import matplotlib.pyplot as plt\n",
    "import utilities as util\n",
    "import analysisfx as analysis\n",
    "\n",
    "# ignore depreciation warnings in this code\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66bab267-ed19-4cc2-896d-22151daeb02c",
   "metadata": {},
   "source": [
    "# Load & Organize Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "308be93e-bcb5-4296-9ede-399a29de9512",
   "metadata": {},
   "source": [
    "### Berkeley daily maximum temperatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3023bf48-8a6d-4599-80ac-481b37ef474c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the berkeley daily maximum temperature data pathway\n",
    "berkdpath='./data/berkeley/Berkeley_TMAX_land_188001_201712_daily_N96_365days_degC.nc'\n",
    "# load in the daily maximum temperature rasters \n",
    "bddat=xr.open_dataset(berkdpath)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a79b7f5-18e9-488a-9d94-524f05f793aa",
   "metadata": {},
   "source": [
    "#### Organize time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d1c68d4e-fc2f-4ecb-bbfa-ff3bc8bf2ffc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create the datetime grid for Berkeley monthly and daily data\n",
    "timegridbd=util.get_dt64(bddat)\n",
    "\n",
    "# add these back into the data structures\n",
    "bddat['time']=timegridbd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66a011fb-ff4a-4aa7-bbc6-788064c8b2aa",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Replace 90S invalid data with missing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a71327ca-4688-4e4a-9d3b-295274c84764",
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   "outputs": [],
   "source": [
    "# set 90S equal to missing\n",
    "bddat=util.set_N96_SouthPole_missing(bddat,'TMAX')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e064356-fd9a-4cab-ae94-4c01314ca920",
   "metadata": {},
   "source": [
    "### GMST (global monthly timeseries, 3-year mean filtered via hadcrut_GMST.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8afea7f3-f624-4577-b330-729f84c2df65",
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   "outputs": [],
   "source": [
    "# load the data\n",
    "gmstpath='./data/analysis/GMST-3yrmean.nc'\n",
    "gmst = xr.open_dataset(gmstpath)"
   ]
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   "cell_type": "markdown",
   "id": "6ffad04b-aba0-4a74-ad5c-7fe53f0cdbb8",
   "metadata": {},
   "source": [
    "## Load Median Scale Factors"
   ]
  },
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   "cell_type": "code",
   "execution_count": 6,
   "id": "8732c9f4-abc1-45da-a5ba-4fc14bec4936",
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   "source": [
    "# define the paths to the load the scale factors from\n",
    "q50_beta_loadpath='./data/analysis/q50_beta.nc'\n",
    "qxx_beta_loadpath='./data/analysis/qxx_mon{month:02d}_beta.nc'\n",
    "\n",
    "# load the scale factors\n",
    "# median-derived\n",
    "q50_beta=xr.open_dataset(q50_beta_loadpath)\n",
    "\n",
    "# (define the months array from loaded data)\n",
    "monthsi=np.asarray(q50_beta.month.values)\n"
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   "cell_type": "markdown",
   "id": "2a3caf01-0c33-4b65-acca-708ea21317d0",
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   "source": [
    "# Find scenario Deltas from HadCRUT5 data"
   ]
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   "cell_type": "markdown",
   "id": "a75515ea-7e24-401c-afc2-190b74584e58",
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   "source": [
    "The scenarios for average temperature are:\n",
    "* Counterfactual (1885-1915)\n",
    "* Climate Base Period (1985-2015)\n",
    "* IPCC Attributable Warming (2010-2019)\n",
    "\n",
    "These periods and their relative global mean temperature anomalies will be used to, in part, drive the observation-based scaling method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f6cd6291-9c53-4e72-99aa-9a0c9a7dbd1b",
   "metadata": {},
   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counterfactual GMST (1885-1915) anomaly from CLIM (1985-2015): -0.85C\n",
      "IPCC Attributable Warming GMST (2010-2019) anomaly from CLIM (1985-2015): 0.29C\n",
      "IPCC Attributable Warming minus Natural: +1.13C\n"
     ]
    }
   ],
   "source": [
    "# calculate differences between periods\n",
    "cf_shift=(gmst['Counterfactual_Delta']-gmst['CLIM_Delta']).values.flatten()[0]\n",
    "forced_shift=(gmst['Attributable_Delta']-gmst['CLIM_Delta']).values.flatten()[0]\n",
    "# and print results to screen\n",
    "print('Counterfactual GMST (1885-1915) anomaly from CLIM (1985-2015): '+str(np.round(cf_shift,2))+'C')\n",
    "print('IPCC Attributable Warming GMST (2010-2019) anomaly from CLIM (1985-2015): '+str(np.round(forced_shift,2))+'C')\n",
    "diff_ATT_minus_CF=forced_shift-cf_shift\n",
    "print('IPCC Attributable Warming minus Natural: +'+str(np.round(diff_ATT_minus_CF,2))+'C')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0288334-3773-4d28-89f1-9aca78e2d0a9",
   "metadata": {},
   "source": [
    "### Define the Climatological Distribution (CLIM) from Observed Berkeley Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bc9c893-4002-4b44-83ca-1b6f34083417",
   "metadata": {},
   "source": [
    "Let's load/define the Climatological distribution of maximum temperatures from 1985-2015."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e96bae81-e634-4c73-aa94-84e3c24d9ac4",
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   "outputs": [
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       "Coordinates:\n",
       "  * lat      (lat) float64 -90.0 -88.75 -87.5 -86.25 ... 86.25 87.5 88.75 90.0\n",
       "  * lon      (lon) float64 0.0 1.875 3.75 5.625 7.5 ... 352.5 354.4 356.2 358.1\n",
       "  * time     (time) datetime64[ns] 1985-01-01 1985-01-02 ... 2015-12-31\n",
       "Data variables:\n",
       "    TMAX     (time, lat, lon) float32 nan nan nan nan nan ... nan nan nan nan\n",
       "Attributes:\n",
       "    standard_name:  surface_temperature_anomaly\n",
       "    long_name:      Air Surface Temperature\n",
       "    units:          degree C</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-4a1a06b9-5688-4a13-9b69-3b482a0dff9e' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-4a1a06b9-5688-4a13-9b69-3b482a0dff9e' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>lat</span>: 145</li><li><span class='xr-has-index'>lon</span>: 192</li><li><span class='xr-has-index'>time</span>: 11315</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-174e66b6-4e66-4615-90fd-56a380d420e2' class='xr-section-summary-in' type='checkbox'  checked><label for='section-174e66b6-4e66-4615-90fd-56a380d420e2' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>lat</span></div><div class='xr-var-dims'>(lat)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-90.0 -88.75 -87.5 ... 88.75 90.0</div><input id='attrs-7055efcf-b47e-4625-b9cd-7695ac904421' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-7055efcf-b47e-4625-b9cd-7695ac904421' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c5936d3c-6a33-4c2e-a820-00ff7554217a' class='xr-var-data-in' type='checkbox'><label for='data-c5936d3c-6a33-4c2e-a820-00ff7554217a' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'><dt><span>standard_name :</span></dt><dd>latitude</dd><dt><span>long_name :</span></dt><dd>latitude</dd><dt><span>units :</span></dt><dd>degrees_north</dd><dt><span>axis :</span></dt><dd>Y</dd></dl></div><div class='xr-var-data'><pre>array([-90.  , -88.75, -87.5 , -86.25, -85.  , -83.75, -82.5 , -81.25, -80.  ,\n",
       "       -78.75, -77.5 , -76.25, -75.  , -73.75, -72.5 , -71.25, -70.  , -68.75,\n",
       "       -67.5 , -66.25, -65.  , -63.75, -62.5 , -61.25, -60.  , -58.75, -57.5 ,\n",
       "       -56.25, -55.  , -53.75, -52.5 , -51.25, -50.  , -48.75, -47.5 , -46.25,\n",
       "       -45.  , -43.75, -42.5 , -41.25, -40.  , -38.75, -37.5 , -36.25, -35.  ,\n",
       "       -33.75, -32.5 , -31.25, -30.  , -28.75, -27.5 , -26.25, -25.  , -23.75,\n",
       "       -22.5 , -21.25, -20.  , -18.75, -17.5 , -16.25, -15.  , -13.75, -12.5 ,\n",
       "       -11.25, -10.  ,  -8.75,  -7.5 ,  -6.25,  -5.  ,  -3.75,  -2.5 ,  -1.25,\n",
       "         0.  ,   1.25,   2.5 ,   3.75,   5.  ,   6.25,   7.5 ,   8.75,  10.  ,\n",
       "        11.25,  12.5 ,  13.75,  15.  ,  16.25,  17.5 ,  18.75,  20.  ,  21.25,\n",
       "        22.5 ,  23.75,  25.  ,  26.25,  27.5 ,  28.75,  30.  ,  31.25,  32.5 ,\n",
       "        33.75,  35.  ,  36.25,  37.5 ,  38.75,  40.  ,  41.25,  42.5 ,  43.75,\n",
       "        45.  ,  46.25,  47.5 ,  48.75,  50.  ,  51.25,  52.5 ,  53.75,  55.  ,\n",
       "        56.25,  57.5 ,  58.75,  60.  ,  61.25,  62.5 ,  63.75,  65.  ,  66.25,\n",
       "        67.5 ,  68.75,  70.  ,  71.25,  72.5 ,  73.75,  75.  ,  76.25,  77.5 ,\n",
       "        78.75,  80.  ,  81.25,  82.5 ,  83.75,  85.  ,  86.25,  87.5 ,  88.75,\n",
       "        90.  ])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>lon</span></div><div class='xr-var-dims'>(lon)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 1.875 3.75 ... 356.2 358.1</div><input id='attrs-32c8b5d8-090a-4bbf-b22b-2731453fad6f' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-32c8b5d8-090a-4bbf-b22b-2731453fad6f' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-1d30866c-b5e0-4ee3-b214-94863b9fac7b' class='xr-var-data-in' type='checkbox'><label for='data-1d30866c-b5e0-4ee3-b214-94863b9fac7b' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'><dt><span>standard_name :</span></dt><dd>longitude</dd><dt><span>long_name :</span></dt><dd>longitude</dd><dt><span>units :</span></dt><dd>degrees_east</dd><dt><span>axis :</span></dt><dd>X</dd></dl></div><div class='xr-var-data'><pre>array([  0.   ,   1.875,   3.75 ,   5.625,   7.5  ,   9.375,  11.25 ,  13.125,\n",
       "        15.   ,  16.875,  18.75 ,  20.625,  22.5  ,  24.375,  26.25 ,  28.125,\n",
       "        30.   ,  31.875,  33.75 ,  35.625,  37.5  ,  39.375,  41.25 ,  43.125,\n",
       "        45.   ,  46.875,  48.75 ,  50.625,  52.5  ,  54.375,  56.25 ,  58.125,\n",
       "        60.   ,  61.875,  63.75 ,  65.625,  67.5  ,  69.375,  71.25 ,  73.125,\n",
       "        75.   ,  76.875,  78.75 ,  80.625,  82.5  ,  84.375,  86.25 ,  88.125,\n",
       "        90.   ,  91.875,  93.75 ,  95.625,  97.5  ,  99.375, 101.25 , 103.125,\n",
       "       105.   , 106.875, 108.75 , 110.625, 112.5  , 114.375, 116.25 , 118.125,\n",
       "       120.   , 121.875, 123.75 , 125.625, 127.5  , 129.375, 131.25 , 133.125,\n",
       "       135.   , 136.875, 138.75 , 140.625, 142.5  , 144.375, 146.25 , 148.125,\n",
       "       150.   , 151.875, 153.75 , 155.625, 157.5  , 159.375, 161.25 , 163.125,\n",
       "       165.   , 166.875, 168.75 , 170.625, 172.5  , 174.375, 176.25 , 178.125,\n",
       "       180.   , 181.875, 183.75 , 185.625, 187.5  , 189.375, 191.25 , 193.125,\n",
       "       195.   , 196.875, 198.75 , 200.625, 202.5  , 204.375, 206.25 , 208.125,\n",
       "       210.   , 211.875, 213.75 , 215.625, 217.5  , 219.375, 221.25 , 223.125,\n",
       "       225.   , 226.875, 228.75 , 230.625, 232.5  , 234.375, 236.25 , 238.125,\n",
       "       240.   , 241.875, 243.75 , 245.625, 247.5  , 249.375, 251.25 , 253.125,\n",
       "       255.   , 256.875, 258.75 , 260.625, 262.5  , 264.375, 266.25 , 268.125,\n",
       "       270.   , 271.875, 273.75 , 275.625, 277.5  , 279.375, 281.25 , 283.125,\n",
       "       285.   , 286.875, 288.75 , 290.625, 292.5  , 294.375, 296.25 , 298.125,\n",
       "       300.   , 301.875, 303.75 , 305.625, 307.5  , 309.375, 311.25 , 313.125,\n",
       "       315.   , 316.875, 318.75 , 320.625, 322.5  , 324.375, 326.25 , 328.125,\n",
       "       330.   , 331.875, 333.75 , 335.625, 337.5  , 339.375, 341.25 , 343.125,\n",
       "       345.   , 346.875, 348.75 , 350.625, 352.5  , 354.375, 356.25 , 358.125])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>time</span></div><div class='xr-var-dims'>(time)</div><div class='xr-var-dtype'>datetime64[ns]</div><div class='xr-var-preview xr-preview'>1985-01-01 ... 2015-12-31</div><input id='attrs-5dde4931-4932-4303-8ee2-8c79189f45af' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-5dde4931-4932-4303-8ee2-8c79189f45af' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-06bda14f-777e-4404-a742-5d7b4c37b44a' class='xr-var-data-in' type='checkbox'><label for='data-06bda14f-777e-4404-a742-5d7b4c37b44a' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;1985-01-01T00:00:00.000000000&#x27;, &#x27;1985-01-02T00:00:00.000000000&#x27;,\n",
       "       &#x27;1985-01-03T00:00:00.000000000&#x27;, ..., &#x27;2015-12-29T00:00:00.000000000&#x27;,\n",
       "       &#x27;2015-12-30T00:00:00.000000000&#x27;, &#x27;2015-12-31T00:00:00.000000000&#x27;],\n",
       "      dtype=&#x27;datetime64[ns]&#x27;)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f0e97c3b-79bd-4279-935f-27fb3bb60f59' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f0e97c3b-79bd-4279-935f-27fb3bb60f59' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>TMAX</span></div><div class='xr-var-dims'>(time, lat, lon)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>nan nan nan nan ... nan nan nan nan</div><input id='attrs-ba9787e4-1c00-4b9c-8c77-f618c7d59c55' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-ba9787e4-1c00-4b9c-8c77-f618c7d59c55' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-60842b27-b2ab-4fa0-8326-4328e0fc34ab' class='xr-var-data-in' type='checkbox'><label for='data-60842b27-b2ab-4fa0-8326-4328e0fc34ab' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'><dt><span>standard_name :</span></dt><dd>surface_temperature_anomaly</dd><dt><span>long_name :</span></dt><dd>Air Surface Temperature</dd><dt><span>units :</span></dt><dd>degree C</dd></dl></div><div class='xr-var-data'><pre>array([[[       nan,        nan,        nan, ...,        nan,\n",
       "                nan,        nan],\n",
       "        [-14.192657, -14.2012  , -14.207642, ..., -14.185627,\n",
       "         -14.181056, -14.184916],\n",
       "        [-13.203035, -13.217878, -13.297653, ..., -13.291447,\n",
       "         -13.261794, -13.229329],\n",
       "        ...,\n",
       "        [       nan,        nan,        nan, ...,        nan,\n",
       "                nan,        nan],\n",
       "        [       nan,        nan,        nan, ...,        nan,\n",
       "                nan,        nan],\n",
       "        [       nan,        nan,        nan, ...,        nan,\n",
       "                nan,        nan]],\n",
       "\n",
       "       [[       nan,        nan,        nan, ...,        nan,\n",
       "                nan,        nan],\n",
       "        [-20.101131, -20.109045, -20.11437 , ..., -20.093338,\n",
       "         -20.089506, -20.093628],\n",
       "        [-18.563414, -18.573645, -18.644314, ..., -18.627466,\n",
       "         -18.607302, -18.584227],\n",
       "...\n",
       "        [       nan,        nan,        nan, ...,        nan,\n",
       "                nan,        nan],\n",
       "        [       nan,        nan,        nan, ...,        nan,\n",
       "                nan,        nan],\n",
       "        [       nan,        nan,        nan, ...,        nan,\n",
       "                nan,        nan]],\n",
       "\n",
       "       [[       nan,        nan,        nan, ...,        nan,\n",
       "                nan,        nan],\n",
       "        [-23.51906 , -23.51389 , -23.505726, ..., -23.548298,\n",
       "         -23.532562, -23.524315],\n",
       "        [-21.635263, -21.609467, -21.642643, ..., -21.774761,\n",
       "         -21.732231, -21.68493 ],\n",
       "        ...,\n",
       "        [       nan,        nan,        nan, ...,        nan,\n",
       "                nan,        nan],\n",
       "        [       nan,        nan,        nan, ...,        nan,\n",
       "                nan,        nan],\n",
       "        [       nan,        nan,        nan, ...,        nan,\n",
       "                nan,        nan]]], dtype=float32)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-b93fa200-b660-42ca-a77c-80062457cecc' class='xr-section-summary-in' type='checkbox'  checked><label for='section-b93fa200-b660-42ca-a77c-80062457cecc' class='xr-section-summary' >Attributes: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>standard_name :</span></dt><dd>surface_temperature_anomaly</dd><dt><span>long_name :</span></dt><dd>Air Surface Temperature</dd><dt><span>units :</span></dt><dd>degree C</dd></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:  (lat: 145, lon: 192, time: 11315)\n",
       "Coordinates:\n",
       "  * lat      (lat) float64 -90.0 -88.75 -87.5 -86.25 ... 86.25 87.5 88.75 90.0\n",
       "  * lon      (lon) float64 0.0 1.875 3.75 5.625 7.5 ... 352.5 354.4 356.2 358.1\n",
       "  * time     (time) datetime64[ns] 1985-01-01 1985-01-02 ... 2015-12-31\n",
       "Data variables:\n",
       "    TMAX     (time, lat, lon) float32 nan nan nan nan nan ... nan nan nan nan\n",
       "Attributes:\n",
       "    standard_name:  surface_temperature_anomaly\n",
       "    long_name:      Air Surface Temperature\n",
       "    units:          degree C"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# find the baseline distribution (1985-2015), subselect that daily distribution\n",
    "CLIMperiod=[1985,2015]\n",
    "CLIM_slice=util.dt64_yrslice(CLIMperiod[0],CLIMperiod[1])\n",
    "CLIMdist=bddat.sel(time=CLIM_slice)\n",
    "\n",
    "# get the indices associated with each month\n",
    "CLIMmonidx=CLIMdist.groupby('time.month').groups\n",
    "\n",
    "# view the dataset\n",
    "CLIMdist"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0b401a7-83c0-4b57-8054-12da8991f960",
   "metadata": {},
   "source": [
    "# Scale CLIM with Median scale factors ($\\beta_{q_i=0.5}$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a0dc7227-f0ad-49dd-8e32-e33ea0095eeb",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mon index=1\n",
      "mon index=2\n",
      "mon index=3\n",
      "mon index=4\n",
      "mon index=5\n",
      "mon index=6\n",
      "mon index=7\n",
      "mon index=8\n",
      "mon index=9\n",
      "mon index=10\n",
      "mon index=11\n",
      "mon index=12\n"
     ]
    }
   ],
   "source": [
    "# define the location to save the distributions to\n",
    "q50savepath='./data/analysis/q50_mon{month:02d}_scaled_distributions.nc'\n",
    "\n",
    "# loop over the months\n",
    "for mi in monthsi:\n",
    "    \n",
    "    # create monthly distribution from baseline\n",
    "    base=CLIMdist['TMAX'][CLIMmonidx[mi]].rename('CLIM')\n",
    "    \n",
    "    # find the scaling temperature anomalies\n",
    "    scale_Tanom_forced=q50_beta.sel(month=mi)*forced_shift\n",
    "    scale_Tanom_cf=q50_beta.sel(month=mi)*cf_shift\n",
    "    \n",
    "    # scale the distributions\n",
    "    forced=(base+scale_Tanom_forced).rename({'beta':'forced'})\n",
    "    cf=(base+scale_Tanom_cf).rename({'beta':'counterfactual'})\n",
    "    del scale_Tanom_forced, scale_Tanom_cf\n",
    "    \n",
    "    # assign to a single dataset\n",
    "    q50_scaled_dists_mi=xr.Dataset(\n",
    "        {\n",
    "            \"base\": (\n",
    "                (\"time\",\"lat\", \"lon\"),\n",
    "                base.data,\n",
    "            ),\n",
    "            \"forced\": (\n",
    "                (\"time\",\"lat\", \"lon\"),\n",
    "                forced['forced'].data,\n",
    "            ),\n",
    "            \"counterfactual\": (\n",
    "                (\"time\",\"lat\", \"lon\"),\n",
    "                cf['counterfactual'].data,\n",
    "            ),\n",
    "        },\n",
    "        coords={\"lat\": base.lat, \"lon\": base.lon, \"time\": base.time, \"month\": mi},\n",
    "        attrs={\"month\": mi, \"quantile\": q50_beta['quantile'].values,\n",
    "               \"forced_period\": '2010-2019', \"counterfactual_period\": '1885-1915', \n",
    "               \"forced_Tshift\": forced_shift, \"counterfactual_Tshift\": cf_shift, \n",
    "               \"unit\": 'degrees C'\n",
    "              }\n",
    "    )\n",
    "    # add in the month\n",
    "    q50_scaled_dists_mi=q50_scaled_dists_mi.expand_dims('month')\n",
    "    \n",
    "    # clean up\n",
    "    del base, forced, cf\n",
    "\n",
    "    # save out to a netcdf file, now that we have the Q50 data array\n",
    "    q50_scaled_dists_mi.to_netcdf(q50savepath.format(month=mi))\n",
    "    del q50_scaled_dists_mi\n",
    "    \n",
    "    # where are we in the loop?\n",
    "    print('mon index='+str(mi))\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6682387-806d-4662-b612-133716913252",
   "metadata": {},
   "source": [
    "# Scale CLIM with Quantile scale factors ($\\beta_{q_i=\\{0.1,0.4,...,0.96,0.99\\}}$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c0e089de-6704-464f-80f0-62dee059f939",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mon index=1\n",
      "mon index=2\n",
      "mon index=3\n",
      "mon index=4\n",
      "mon index=5\n",
      "mon index=6\n",
      "mon index=7\n",
      "mon index=8\n",
      "mon index=9\n",
      "mon index=10\n",
      "mon index=11\n",
      "mon index=12\n"
     ]
    }
   ],
   "source": [
    "# define a path to load the quantile data from\n",
    "qxx_Tquant_loadpath='./data/berkeley/qxx_mon{month:02d}_1880-2017.nc'\n",
    "\n",
    "# define the location to save the distributions to\n",
    "qxxsavepath='./data/analysis/qxx_mon{month:02d}_scaled_distributions.nc'\n",
    "\n",
    "# quantile-derived (load by month and merge)\n",
    "for mi in monthsi:\n",
    "    \n",
    "    # load the quantiles scaling factor data\n",
    "    qxx_beta_in=xr.open_dataset(qxx_beta_loadpath.format(month=mi))\n",
    "    # ensure month is a correct dimension\n",
    "    if len(qxx_beta_in.dims)==3:\n",
    "        qxx_beta_in=qxx_beta_in.assign_coords(month=mi).expand_dims('month')\n",
    "    # initialize the quantiles we are calculating over\n",
    "    if mi==1:\n",
    "        qi=np.asarray(qxx_beta_in['quantile'].values)\n",
    "        \n",
    "    # load the raw quantile temperature data\n",
    "    qxx_Tquant=xr.open_dataset(qxx_Tquant_loadpath.format(month=mi))\n",
    "    \n",
    "    # initialize the climatology\n",
    "    # create monthly distribution from baseline\n",
    "    base=qxx_Tquant.TMAX.sel(time=CLIM_slice).rename({'CLIM'})\n",
    "        \n",
    "    # find the scaling temperature anomalies\n",
    "    scale_Tanom_forced=qxx_beta_in*forced_shift\n",
    "    scale_Tanom_cf=qxx_beta_in*cf_shift\n",
    "    \n",
    "    # scale the distributions\n",
    "    forced=(base+scale_Tanom_forced).rename({'beta':'forced'}).isel(month=0)\n",
    "    cf=(base+scale_Tanom_cf).rename({'beta':'counterfactual'}).isel(month=0)\n",
    "    del scale_Tanom_forced, scale_Tanom_cf\n",
    "    \n",
    "    # assign to a single dataset\n",
    "    qxx_scaled_dists_mi=xr.Dataset(\n",
    "        {\n",
    "            \"base\": (\n",
    "                (\"time\",\"quantile\",\"lat\", \"lon\"),\n",
    "                base.data,\n",
    "            ),\n",
    "            \"forced\": (\n",
    "                (\"time\",\"quantile\",\"lat\", \"lon\"),\n",
    "                forced['forced'].data,\n",
    "            ),\n",
    "            \"counterfactual\": (\n",
    "                (\"time\",\"quantile\",\"lat\", \"lon\"),\n",
    "                cf['counterfactual'].data,\n",
    "            ),\n",
    "        },\n",
    "        coords={\"lat\": base.lat, \"lon\": base.lon, \"time\": base.time, \"month\": mi},\n",
    "        attrs={\"month\": mi, \"quantile\": qi,\n",
    "               \"forced_period\": '2010-2019', \"counterfactual_period\": '1885-1915', \n",
    "               \"forced_Tshift\": forced_shift, \"counterfactual_Tshift\": cf_shift, \n",
    "               \"unit\": 'degrees C'\n",
    "              }\n",
    "    )\n",
    "    # add in the month\n",
    "    qxx_scaled_dists_mi=qxx_scaled_dists_mi.expand_dims('month')\n",
    "    \n",
    "    # clean up\n",
    "    del base, forced, cf\n",
    "\n",
    "    # save out to a netcdf file, now that we have the Q50 data array\n",
    "    qxx_scaled_dists_mi.to_netcdf(qxxsavepath.format(month=mi))\n",
    "    del qxx_scaled_dists_mi\n",
    "    \n",
    "    # where are we in the loop?\n",
    "    print('mon index='+str(mi))\n",
    "    \n",
    "    # clean up\n",
    "    del qxx_beta_in, qxx_Tquant"
   ]
  },
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   "metadata": {},
   "outputs": [],
   "source": []
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