revision_check_fig3_confidence.ipynb

{
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   "cell_type": "markdown",
   "id": "champion-nashville",
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   "source": [
    "Reviewer 1 asks whether we can really say that, for locking case especially, the change in extreme fraction ($\\phi$) is really larger than the change in the precipitation ($P$). \n",
    "\n",
    "This is a bit tricky, which is why I didn't do it before. \n",
    "\n",
    "We can bootstrap a confidence interval. I guess that we can directly bootstrap the CI for the difference.\n",
    "\n",
    "$X = \\delta \\phi - \\delta P$\n",
    "\n",
    "where $\\delta() = ( ()_2 - ()_1) / ()_1$\n",
    "\n",
    "To get at this, we will calculate a very large number of realizations of $X$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "timely-legend",
   "metadata": {},
   "outputs": [],
   "source": [
    "import xarray as xr\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "from pathlib import Path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "urban-surrey",
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import namedtuple\n",
    "\n",
    "Result = namedtuple('Result', ['case', 'gavg', 'goavg', 'tavg', 'toavg', 'toavg_uw', 'p95', 'tsum', 'xsum'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "recreational-thursday",
   "metadata": {},
   "outputs": [],
   "source": [
    "# locking results:\n",
    "variable = \"PRECT\"\n",
    "\n",
    "tropics = slice(-30,30)\n",
    "\n",
    "cases = {\n",
    "    'f-lock': '/Volumes/Samsung_T5/F1850JJB_c201_CLOCK.cam.h2.ncrcat.PRECT.nc',\n",
    "    'f-cntl': '/Volumes/Samsung_T5/F1850JJB_c201_CTL.cam.h2.ncrcat.PRECT.nc',\n",
    "    'c-lock': '/Volumes/Samsung_T5/B1850_c201_CLOCK/daily/B1850_c201_CLOCK.cam.h2.ncrcat.PRECT.nc',\n",
    "    'c-cntl': '/Volumes/Samsung_T5/B1850_c201_CTL/daily/B1850_c201_CTL.cam.h2.ncrcat.PRECT.nc'}\n",
    "\n",
    "case_names = {'f-lock': 'F1850JJB_c201_CLOCK',\n",
    "    'f-cntl': 'F1850JJB_c201_CTL',\n",
    "    'c-lock': 'B1850_c201_CLOCK',\n",
    "    'c-cntl': 'B1850_c201_CTL'}\n",
    "\n",
    "# f-cntl ntime = 9126\n",
    "# f-lock ntime = 9126\n",
    "# c-cntl ntime = 10982\n",
    "# c-lock ntime = 9491\n",
    "\n",
    "\n",
    "# LAND\n",
    "land_file = xr.open_dataset(\"/Users/brianpm/Dropbox/Data/cesm2_f09_land.nc\")\n",
    "LAND = land_file['LANDFRAC'].squeeze()\n",
    "\n",
    "\n",
    "# First things first, let's just load the data:\n",
    "locking_data = {}\n",
    "for c in cases:\n",
    "    tmp = xr.open_dataset(cases[c])\n",
    "    locking_data[c] = tmp['PRECT'].where(LAND <= 0).sel(lat=tropics)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "furnished-immigration",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 143402956 of data out of possible 202420224 elements\n",
      "(143402956,)\n"
     ]
    }
   ],
   "source": [
    "total_number = locking_data['c-cntl'].values.size\n",
    "valid_number = np.count_nonzero(~np.isnan(locking_data['c-cntl'].values))  # counts the values that aren't nan\n",
    "print(f'There are {valid_number} of data out of possible {total_number} elements')\n",
    "\n",
    "# select the valid values in the flattened array:\n",
    "flt = locking_data['c-cntl'].values.flatten()\n",
    "z = flt[~np.isnan(flt)]\n",
    "# 143 million points -- let's take a sample of 100million w/replacement"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "twenty-selection",
   "metadata": {},
   "source": [
    "So we have the tropical ocean data for each case in locking_data. \n",
    "\n",
    "I suppose what we want to do is take only the tropical ocean data (i.e. non-missing points), and take a sample of that data. Calculate all the pieces, i.e. the total precipitation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "amateur-transportation",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "case is f-lock\n",
      "\t ... 0\n",
      "\t ... 100\n",
      "\t ... 200\n",
      "\t ... 300\n",
      "\t ... 400\n",
      "\t ... 500\n",
      "\t ... 600\n",
      "\t ... 700\n",
      "\t ... 800\n",
      "\t ... 900\n",
      "case is f-cntl\n",
      "\t ... 0\n",
      "\t ... 100\n",
      "\t ... 200\n",
      "\t ... 300\n",
      "\t ... 400\n",
      "\t ... 500\n",
      "\t ... 600\n",
      "\t ... 700\n",
      "\t ... 800\n",
      "\t ... 900\n",
      "case is c-lock\n",
      "\t ... 0\n",
      "\t ... 100\n",
      "\t ... 200\n",
      "\t ... 300\n",
      "\t ... 400\n",
      "\t ... 500\n",
      "\t ... 600\n",
      "\t ... 700\n",
      "\t ... 800\n",
      "\t ... 900\n",
      "case is c-cntl\n",
      "\t ... 0\n",
      "\t ... 100\n",
      "\t ... 200\n",
      "\t ... 300\n",
      "\t ... 400\n",
      "\t ... 500\n",
      "\t ... 600\n",
      "\t ... 700\n",
      "\t ... 800\n",
      "\t ... 900\n"
     ]
    }
   ],
   "source": [
    "rng = np.random.default_rng() # instantiate random number generator\n",
    "\n",
    "bootstrap_n = 1000\n",
    "bootstrap_sample_size = np.count_nonzero(~np.isnan(locking_data['c-cntl'].isel(time=0).values))*365*10  # i.e., 10 years of data\n",
    "\n",
    "result = {}\n",
    "for c in cases:\n",
    "    print(f\"case is {c}\")\n",
    "    pbar = np.zeros(bootstrap_n)\n",
    "    phi = np.zeros(bootstrap_n)\n",
    "    q95 = np.zeros(bootstrap_n)\n",
    "    diff = np.zeros(bootstrap_n)\n",
    "    # create the 1-d dataset\n",
    "    z = locking_data[c].values.flatten()\n",
    "    z = z[~np.isnan(z)]\n",
    "    for i in range(bootstrap_n):\n",
    "        if i%100 == 0:\n",
    "            print(f\"\\t ... {i}\")\n",
    "        smpl = rng.choice(z, bootstrap_sample_size, True)\n",
    "        pbar[i] = np.mean(smpl)\n",
    "        q95[i] = np.quantile(smpl, 0.95)\n",
    "        phi[i] = np.nansum(smpl[smpl>q95[i]])/np.nansum(smpl)\n",
    "    result[c] = (pbar, phi)\n",
    "    "
   ]
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   "execution_count": 53,
   "id": "coupled-hebrew",
   "metadata": {},
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   "source": [
    "# since that took a long time, let's put the results into a file\n",
    "for c in result:\n",
    "    d = {\"pr_avg\": {\"dims\": (\"n\"), \"data\": result[c][0]},\n",
    "         \"phi\": {\"dims\": (\"n\"), \"data\": result[c][1]}}\n",
    "    dstmp = xr.Dataset.from_dict(d)\n",
    "    fname = f'/Users/brianpm/Dropbox/Manuscripts/M_cre_pex/bootstrap_phi_{c}.nc'\n",
    "    dstmp.to_netcdf(fname)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "reserved-patch",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For case f-lock, 95% CI on Avg(P) is (3.963155759123538e-08,3.967842383545417e-08), and for phi it is (0.4095747999846935, 0.40995189025998113)\n",
      "For case f-cntl, 95% CI on Avg(P) is (4.0505792142653264e-08,4.0558186675809794e-08), and for phi it is (0.432826142758131, 0.43323486149311063)\n",
      "For case c-lock, 95% CI on Avg(P) is (3.9582340072286115e-08,3.9630223902520355e-08), and for phi it is (0.4172159731388092, 0.4175929225981236)\n",
      "For case c-cntl, 95% CI on Avg(P) is (4.0317178573445746e-08,4.037019492031391e-08), and for phi it is (0.4287880018353462, 0.4291559934616089)\n"
     ]
    }
   ],
   "source": [
    "# get the quantiles for the CI\n",
    "for c in result:\n",
    "    pbar_ci = np.quantile(result[c][0], [0.025, 0.975])\n",
    "    phi_ci = np.quantile(result[c][1], [0.025, 0.975])\n",
    "    print(f\"For case {c}, 95% CI on Avg(P) is ({pbar_ci[0]},{pbar_ci[1]}), and for phi it is ({phi_ci[0]}, {phi_ci[1]})\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "advised-qualification",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean δP = -0.01829927533448693, 95% CI = (-0.019094793578599827, -0.017391924635068473)\n",
      "Mean δϕ = -0.026987462001868356, 95% CI = (-0.02761265832381869, -0.02639860001048672)\n",
      "Mean δϕ - δP = -0.008688186667381423, 95% CI = (-0.009702954683430461, -0.007695971408016631)\n"
     ]
    }
   ],
   "source": [
    "# next calculate the fractional changes\n",
    "delta_p = (result['c-lock'][0] - result['c-cntl'][0]) / result['c-cntl'][0]\n",
    "delta_p_quants = np.quantile(delta_p, [0.025, 0.25, 0.5, 0.75, 0.975])\n",
    "# print(delta_p_quants)\n",
    "mean_dp = np.mean(delta_p)\n",
    "print(f\"Mean δP = {mean_dp}, 95% CI = ({delta_p_quants[0]}, {delta_p_quants[-1]})\")\n",
    "\n",
    "delta_phi = (result['c-lock'][1] - result['c-cntl'][1]) / result['c-cntl'][1]\n",
    "delta_phi_quants = np.quantile(delta_phi, [0.025, 0.25, 0.5, 0.75, 0.975])\n",
    "# print(delta_phi_quants)\n",
    "mean_dphi = np.mean(delta_phi)\n",
    "print(f\"Mean δϕ = {mean_dphi}, 95% CI = ({delta_phi_quants[0]}, {delta_phi_quants[-1]})\")\n",
    "\n",
    "\n",
    "\n",
    "diff = delta_phi - delta_p\n",
    "diff_quants = np.quantile(diff, [0.025, 0.25, 0.5, 0.75, 0.975])\n",
    "# print(diff_quants)\n",
    "mean_diff = np.mean(diff)\n",
    "print(f\"Mean δϕ - δP = {mean_diff}, 95% CI = ({diff_quants[0]}, {diff_quants[-1]})\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "another-transmission",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min: 3.4817, Max:  3.4896, Mean:  3.4857\n",
      "Min: 3.4808, Max:  3.49, Mean:  3.4858\n",
      "Min: 0.42861, Max:  0.42936, Mean:  0.42898\n",
      "Min: 0.42854, Max:  0.42937, Mean:  0.42898\n"
     ]
    }
   ],
   "source": [
    "def printMinMaxMean(z):\n",
    "    print(f\"Min: {np.min(z):0.5g}, Max: {np.max(z): 0.5g}, Mean: {np.mean(z): 0.5g}\")\n",
    "printMinMaxMean((result['f-cntl'][0])*86400.*1000.)\n",
    "printMinMaxMean((result['f-lock'][0])*86400.*1000.)\n",
    "\n",
    "printMinMaxMean((result['f-cntl'][1]))\n",
    "printMinMaxMean((result['f-lock'][1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "unlike-boundary",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "case 1: f-cntl\n",
      "case 2: f-lock\n",
      "get test stats\n",
      "The t-statistic is 77.68819340534756, the p-value is 0.0; If pvalue is small, the means are different. Check True\n"
     ]
    }
   ],
   "source": [
    "# Alternative is to use two-sided t-statistic\n",
    "from scipy import stats\n",
    "\n",
    "# start from the full data, and let's just see if the means are different\n",
    "# tropical ocean, removing the land values from the data\n",
    "case1 = 'f-cntl'\n",
    "case2 = 'f-lock'\n",
    "print(f\"case 1: {case1}\")\n",
    "v1 = locking_data[case1].values.flatten()\n",
    "vs1 = v1[~np.isnan(v1)]\n",
    "print(f\"case 2: {case2}\")\n",
    "v2 = locking_data[case2].values.flatten()\n",
    "vs2 = v2[~np.isnan(v2)]\n",
    "print(\"get test stats\")\n",
    "tstat, pval = stats.ttest_ind(vs1,vs2, equal_var=False)\n",
    "print(f\"The t-statistic is {tstat}, the p-value is {pval}; If pvalue is small, the means are different. Check {pval < 0.05}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "excess-wyoming",
   "metadata": {},
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       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;PRECT&#x27; (time: 9126, lat: 64, lon: 288)&gt;\n",
       "array([[[8.39906181e-15, 9.56331453e-15, 1.38928625e-14, ...,\n",
       "         1.08391859e-14, 1.41338747e-14, 1.46511170e-14],\n",
       "        [9.02741034e-15, 1.01508877e-14, 1.72553571e-14, ...,\n",
       "         1.06547156e-14, 1.15186333e-14, 1.37354626e-14],\n",
       "        [1.54575568e-14, 9.32483833e-15, 1.77080589e-14, ...,\n",
       "         1.10776739e-14, 1.13117777e-14, 1.25204141e-14],\n",
       "        ...,\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan]],\n",
       "\n",
       "       [[3.11407833e-09, 2.77238144e-09, 4.07668699e-09, ...,\n",
       "         1.99464534e-09, 1.90572136e-09, 2.23409780e-09],\n",
       "        [1.73748882e-09, 2.18656115e-09, 3.34102412e-09, ...,\n",
       "         1.87943727e-09, 1.97307570e-09, 2.80684742e-09],\n",
       "        [3.52350771e-09, 3.68159414e-09, 4.37270575e-09, ...,\n",
       "         1.75055381e-09, 2.52436405e-09, 3.20052651e-09],\n",
       "...\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan]],\n",
       "\n",
       "       [[9.52268597e-10, 9.98258143e-10, 5.32153044e-10, ...,\n",
       "         2.35966602e-09, 4.38641878e-09, 2.02308259e-09],\n",
       "        [5.71101166e-10, 9.00992725e-10, 3.42386258e-10, ...,\n",
       "         3.10979154e-09, 2.85298296e-09, 8.87152296e-10],\n",
       "        [3.15290505e-09, 6.22226215e-10, 7.97934607e-10, ...,\n",
       "         3.51245810e-09, 1.24410560e-09, 6.31795727e-10],\n",
       "        ...,\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan]]], dtype=float32)\n",
       "Coordinates:\n",
       "  * lat      (lat) float64 -29.69 -28.74 -27.8 -26.86 ... 26.86 27.8 28.74 29.69\n",
       "  * lon      (lon) float64 0.0 1.25 2.5 3.75 5.0 ... 355.0 356.2 357.5 358.8\n",
       "  * time     (time) object 0003-01-01 00:00:00 ... 0028-01-01 00:00:00\n",
       "Attributes:\n",
       "    units:         m/s\n",
       "    long_name:     Total (convective and large-scale) precipitation rate (liq...\n",
       "    cell_methods:  time: mean</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'PRECT'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>time</span>: 9126</li><li><span class='xr-has-index'>lat</span>: 64</li><li><span class='xr-has-index'>lon</span>: 288</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-d0a65a00-722a-48f5-a7d3-b878b15ecc3a' class='xr-array-in' type='checkbox' checked><label for='section-d0a65a00-722a-48f5-a7d3-b878b15ecc3a' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>8.399e-15 9.563e-15 1.389e-14 1.499e-14 1.111e-14 ... nan nan nan nan</span></div><div class='xr-array-data'><pre>array([[[8.39906181e-15, 9.56331453e-15, 1.38928625e-14, ...,\n",
       "         1.08391859e-14, 1.41338747e-14, 1.46511170e-14],\n",
       "        [9.02741034e-15, 1.01508877e-14, 1.72553571e-14, ...,\n",
       "         1.06547156e-14, 1.15186333e-14, 1.37354626e-14],\n",
       "        [1.54575568e-14, 9.32483833e-15, 1.77080589e-14, ...,\n",
       "         1.10776739e-14, 1.13117777e-14, 1.25204141e-14],\n",
       "        ...,\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan]],\n",
       "\n",
       "       [[3.11407833e-09, 2.77238144e-09, 4.07668699e-09, ...,\n",
       "         1.99464534e-09, 1.90572136e-09, 2.23409780e-09],\n",
       "        [1.73748882e-09, 2.18656115e-09, 3.34102412e-09, ...,\n",
       "         1.87943727e-09, 1.97307570e-09, 2.80684742e-09],\n",
       "        [3.52350771e-09, 3.68159414e-09, 4.37270575e-09, ...,\n",
       "         1.75055381e-09, 2.52436405e-09, 3.20052651e-09],\n",
       "...\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan]],\n",
       "\n",
       "       [[9.52268597e-10, 9.98258143e-10, 5.32153044e-10, ...,\n",
       "         2.35966602e-09, 4.38641878e-09, 2.02308259e-09],\n",
       "        [5.71101166e-10, 9.00992725e-10, 3.42386258e-10, ...,\n",
       "         3.10979154e-09, 2.85298296e-09, 8.87152296e-10],\n",
       "        [3.15290505e-09, 6.22226215e-10, 7.97934607e-10, ...,\n",
       "         3.51245810e-09, 1.24410560e-09, 6.31795727e-10],\n",
       "        ...,\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan]]], dtype=float32)</pre></div></div></li><li class='xr-section-item'><input id='section-7c0c648d-6004-474f-9697-6599e1a6f193' class='xr-section-summary-in' type='checkbox'  checked><label for='section-7c0c648d-6004-474f-9697-6599e1a6f193' 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'>-29.69 -28.74 -27.8 ... 28.74 29.69</div><input id='attrs-20289b07-95fb-45d1-bb6b-fca6673fd943' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-20289b07-95fb-45d1-bb6b-fca6673fd943' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-39dc9b18-1cc0-45ab-95cf-208bc3f7dbb4' class='xr-var-data-in' type='checkbox'><label for='data-39dc9b18-1cc0-45ab-95cf-208bc3f7dbb4' 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>long_name :</span></dt><dd>latitude</dd><dt><span>units :</span></dt><dd>degrees_north</dd></dl></div><div class='xr-var-data'><pre>array([-29.685864, -28.743455, -27.801047, -26.858639, -25.91623 , -24.973822,\n",
       "       -24.031414, -23.089005, -22.146597, -21.204188, -20.26178 , -19.319372,\n",
       "       -18.376963, -17.434555, -16.492147, -15.549738, -14.60733 , -13.664921,\n",
       "       -12.722513, -11.780105, -10.837696,  -9.895288,  -8.95288 ,  -8.010471,\n",
       "        -7.068063,  -6.125654,  -5.183246,  -4.240838,  -3.298429,  -2.356021,\n",
       "        -1.413613,  -0.471204,   0.471204,   1.413613,   2.356021,   3.298429,\n",
       "         4.240838,   5.183246,   6.125654,   7.068063,   8.010471,   8.95288 ,\n",
       "         9.895288,  10.837696,  11.780105,  12.722513,  13.664921,  14.60733 ,\n",
       "        15.549738,  16.492147,  17.434555,  18.376963,  19.319372,  20.26178 ,\n",
       "        21.204188,  22.146597,  23.089005,  24.031414,  24.973822,  25.91623 ,\n",
       "        26.858639,  27.801047,  28.743455,  29.685864])</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 1.25 2.5 ... 356.2 357.5 358.8</div><input id='attrs-380aff90-fa62-4dc4-9dd1-066f87d6b0cc' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-380aff90-fa62-4dc4-9dd1-066f87d6b0cc' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-49be79a6-b3ea-4f62-87b2-38d87e37d1e6' class='xr-var-data-in' type='checkbox'><label for='data-49be79a6-b3ea-4f62-87b2-38d87e37d1e6' 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>long_name :</span></dt><dd>longitude</dd><dt><span>units :</span></dt><dd>degrees_east</dd></dl></div><div class='xr-var-data'><pre>array([  0.  ,   1.25,   2.5 , ..., 356.25, 357.5 , 358.75])</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'>object</div><div class='xr-var-preview xr-preview'>0003-01-01 00:00:00 ... 0028-01-...</div><input id='attrs-6fbc352e-0ee7-4ede-b9ff-498b93f25264' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-6fbc352e-0ee7-4ede-b9ff-498b93f25264' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-241555d8-4058-4895-83cb-253de26f8b22' class='xr-var-data-in' type='checkbox'><label for='data-241555d8-4058-4895-83cb-253de26f8b22' 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>long_name :</span></dt><dd>time</dd><dt><span>bounds :</span></dt><dd>time_bnds</dd></dl></div><div class='xr-var-data'><pre>array([cftime.DatetimeNoLeap(3, 1, 1, 0, 0, 0, 0),\n",
       "       cftime.DatetimeNoLeap(3, 1, 2, 0, 0, 0, 0),\n",
       "       cftime.DatetimeNoLeap(3, 1, 3, 0, 0, 0, 0), ...,\n",
       "       cftime.DatetimeNoLeap(27, 12, 30, 0, 0, 0, 0),\n",
       "       cftime.DatetimeNoLeap(27, 12, 31, 0, 0, 0, 0),\n",
       "       cftime.DatetimeNoLeap(28, 1, 1, 0, 0, 0, 0)], dtype=object)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-949a6987-8133-4ff7-a23c-183f8bd7c8fa' class='xr-section-summary-in' type='checkbox'  checked><label for='section-949a6987-8133-4ff7-a23c-183f8bd7c8fa' 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>units :</span></dt><dd>m/s</dd><dt><span>long_name :</span></dt><dd>Total (convective and large-scale) precipitation rate (liq + ice)</dd><dt><span>cell_methods :</span></dt><dd>time: mean</dd></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'PRECT' (time: 9126, lat: 64, lon: 288)>\n",
       "array([[[8.39906181e-15, 9.56331453e-15, 1.38928625e-14, ...,\n",
       "         1.08391859e-14, 1.41338747e-14, 1.46511170e-14],\n",
       "        [9.02741034e-15, 1.01508877e-14, 1.72553571e-14, ...,\n",
       "         1.06547156e-14, 1.15186333e-14, 1.37354626e-14],\n",
       "        [1.54575568e-14, 9.32483833e-15, 1.77080589e-14, ...,\n",
       "         1.10776739e-14, 1.13117777e-14, 1.25204141e-14],\n",
       "        ...,\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan]],\n",
       "\n",
       "       [[3.11407833e-09, 2.77238144e-09, 4.07668699e-09, ...,\n",
       "         1.99464534e-09, 1.90572136e-09, 2.23409780e-09],\n",
       "        [1.73748882e-09, 2.18656115e-09, 3.34102412e-09, ...,\n",
       "         1.87943727e-09, 1.97307570e-09, 2.80684742e-09],\n",
       "        [3.52350771e-09, 3.68159414e-09, 4.37270575e-09, ...,\n",
       "         1.75055381e-09, 2.52436405e-09, 3.20052651e-09],\n",
       "...\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan]],\n",
       "\n",
       "       [[9.52268597e-10, 9.98258143e-10, 5.32153044e-10, ...,\n",
       "         2.35966602e-09, 4.38641878e-09, 2.02308259e-09],\n",
       "        [5.71101166e-10, 9.00992725e-10, 3.42386258e-10, ...,\n",
       "         3.10979154e-09, 2.85298296e-09, 8.87152296e-10],\n",
       "        [3.15290505e-09, 6.22226215e-10, 7.97934607e-10, ...,\n",
       "         3.51245810e-09, 1.24410560e-09, 6.31795727e-10],\n",
       "        ...,\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan],\n",
       "        [           nan,            nan,            nan, ...,\n",
       "                    nan,            nan,            nan]]], dtype=float32)\n",
       "Coordinates:\n",
       "  * lat      (lat) float64 -29.69 -28.74 -27.8 -26.86 ... 26.86 27.8 28.74 29.69\n",
       "  * lon      (lon) float64 0.0 1.25 2.5 3.75 5.0 ... 355.0 356.2 357.5 358.8\n",
       "  * time     (time) object 0003-01-01 00:00:00 ... 0028-01-01 00:00:00\n",
       "Attributes:\n",
       "    units:         m/s\n",
       "    long_name:     Total (convective and large-scale) precipitation rate (liq...\n",
       "    cell_methods:  time: mean"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "locking_data['f-cntl']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "national-salmon",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def get_cesm_pr_info(fil, experiment, land=None):\n",
    "    tropics = slice(-30,30)\n",
    "    pr_ds = xr.open_dataset(fil)\n",
    "    pr = pr_ds['PRECT']*1000. # converts to same units as CMIP6 pr\n",
    "    lat = pr['lat']\n",
    "    wgt = np.cos(np.radians(lat))\n",
    "    gavg = esmlab.weighted_mean(pr.mean(dim=('time','lon')), dim=[\"lat\"], weights=wgt).item()\n",
    "    tavg = esmlab.weighted_mean(pr.sel(lat=tropics).mean(dim=('time','lon')), dim=[\"lat\"], weights=wgt.sel(lat=tropics)).item()\n",
    "    if land is not None:\n",
    "        land_trop = land.sel(lat=tropics)\n",
    "        msk, _ = xr.broadcast(land, pr)\n",
    "        pr = pr.where(msk <= 0)\n",
    "        goavg = esmlab.weighted_mean(pr.mean(dim=('time','lon')), dim=[\"lat\"], weights=wgt).item()\n",
    "        toavg = esmlab.weighted_mean(pr.sel(lat=tropics).mean(dim=('time','lon')), dim=[\"lat\"], weights=wgt.sel(lat=tropics)).item()\n",
    "    else:\n",
    "        goavg = gavg\n",
    "        toavg = tavg\n",
    "    ptrop = pr.sel(lat=tropics)\n",
    "    toavg_uw = ptrop.mean().item()\n",
    "    p95 = np.nanquantile(ptrop.values.flatten(), 0.95)\n",
    "    tsum = np.nansum(ptrop.values.flatten())\n",
    "    xsum = np.nansum(ptrop.where(ptrop>=p95).values.flatten())\n",
    "    return Result(experiment, gavg, goavg, tavg, toavg, toavg_uw, p95, tsum, xsum)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "strong-trash",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.],\n",
       "       [-1.,  0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.],\n",
       "       [-2., -1.,  0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.],\n",
       "       [-3., -2., -1.,  0.,  1.,  2.,  3.,  4.,  5.,  6.],\n",
       "       [-4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.,  5.],\n",
       "       [-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.],\n",
       "       [-6., -5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.],\n",
       "       [-7., -6., -5., -4., -3., -2., -1.,  0.,  1.,  2.],\n",
       "       [-8., -7., -6., -5., -4., -3., -2., -1.,  0.,  1.],\n",
       "       [-9., -8., -7., -6., -5., -4., -3., -2., -1.,  0.]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.outer(np.ones(10), np.arange(1, 11)) - np.outer(np.arange(1, 11), np.ones(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "hollow-caribbean",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.],\n",
       "       [ 2.,  2.,  2.,  2.,  2.,  2.,  2.,  2.,  2.,  2.],\n",
       "       [ 3.,  3.,  3.,  3.,  3.,  3.,  3.,  3.,  3.,  3.],\n",
       "       [ 4.,  4.,  4.,  4.,  4.,  4.,  4.,  4.,  4.,  4.],\n",
       "       [ 5.,  5.,  5.,  5.,  5.,  5.,  5.,  5.,  5.,  5.],\n",
       "       [ 6.,  6.,  6.,  6.,  6.,  6.,  6.,  6.,  6.,  6.],\n",
       "       [ 7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.],\n",
       "       [ 8.,  8.,  8.,  8.,  8.,  8.,  8.,  8.,  8.,  8.],\n",
       "       [ 9.,  9.,  9.,  9.,  9.,  9.,  9.,  9.,  9.,  9.],\n",
       "       [10., 10., 10., 10., 10., 10., 10., 10., 10., 10.]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "organizational-victorian",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
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  "language_info": {
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