Correlation Length.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4c748963",
   "metadata": {},
   "outputs": [],
   "source": [
    "#In this piece of code we the gyration radius and the mean size cluster for a number of elevations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "received-symphony",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Libraries\n",
    "from pylab import *\n",
    "from scipy.ndimage import measurements\n",
    "import numba\n",
    "from netCDF4 import Dataset\n",
    "import numpy as np\n",
    "import os\n",
    "from tqdm import tqdm\n",
    "from scipy.ndimage import measurements\n",
    "import time\n",
    "import sympy\n",
    "import concurrent.futures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "polish-smooth",
   "metadata": {},
   "outputs": [],
   "source": [
    "#the function for loading the orginal data. we used Ryota Kiuchi which you can find here:https://towardsdatascience.com/create-interactive-globe-earthquake-plot-in-python-b0b52b646f27\n",
    "def Etopo(lon_area, lat_area, resolution):\n",
    "    ### Input\n",
    "    # resolution: resolution of topography for both of longitude and latitude [deg]\n",
    "    # (Original resolution is 0.0167 deg)\n",
    "    # lon_area and lat_area: the region of the map which you want like [100, 130], [20, 25]\n",
    "    ###\n",
    "    ### Output\n",
    "    # Mesh type longitude, latitude, and topography data\n",
    "    ###\n",
    "\n",
    "    # Read NetCDF data\n",
    "    data = Dataset(\"ETOPO1_Bed_c_gdal.grd\", \"r\")\n",
    "    # Get data\n",
    "    lon_range = data.variables['x_range'][:]\n",
    "    lat_range = data.variables['y_range'][:]\n",
    "    topo_range = data.variables['z_range'][:]\n",
    "    spacing = data.variables['spacing'][:]\n",
    "    dimension = data.variables['dimension'][:]\n",
    "    z = data.variables['z'][:]\n",
    "    lon_num = dimension[0]\n",
    "    lat_num = dimension[1]\n",
    "  \n",
    "    # Prepare array\n",
    "    lon_input = np.zeros(lon_num); lat_input = np.zeros(lat_num)\n",
    "    for i in range(lon_num):\n",
    "        lon_input[i] = lon_range[0] + i * spacing[0]\n",
    "    for i in range(lat_num):\n",
    "        lat_input[i] = lat_range[0] + i * spacing[1]\n",
    "\n",
    "    # Create 2D array\n",
    "    lon, lat = np.meshgrid(lon_input, lat_input)\n",
    "\n",
    "    # Convert 2D array from 1D array for z value\n",
    "    topo = np.reshape(z, (lat_num, lon_num))\n",
    "  \n",
    "    # Skip the data for resolution\n",
    "    if ((resolution < spacing[0]) | (resolution < spacing[1])):\n",
    "        print('Set the highest resolution')\n",
    "    else:\n",
    "        skip = int(resolution/spacing[0])\n",
    "        lon = lon[::skip,::skip]\n",
    "        lat = lat[::skip,::skip]\n",
    "        topo = topo[::skip,::skip]\n",
    "\n",
    "    topo = topo[::-1]\n",
    "  \n",
    "    # Select the range of map\n",
    "    range1 = np.where((lon>=lon_area[0]) & (lon<=lon_area[1]))\n",
    "    lon = lon[range1]; lat = lat[range1]; topo = topo[range1]\n",
    "    range2 = np.where((lat>=lat_area[0]) & (lat<=lat_area[1]))\n",
    "    lon = lon[range2]; lat = lat[range2]; topo = topo[range2]\n",
    "  \n",
    "    # Convert 2D again\n",
    "    lon_num = len(np.unique(lon))\n",
    "    lat_num = len(np.unique(lat))\n",
    "    lon = np.reshape(lon, (lat_num, lon_num))\n",
    "    lat = np.reshape(lat, (lat_num, lon_num))\n",
    "    topo = np.reshape(topo, (lat_num, lon_num))\n",
    "\n",
    "    return lon, lat, topo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "virtual-mining",
   "metadata": {},
   "outputs": [],
   "source": [
    "# convert degrees to radians\n",
    "def degree2radians(degree):\n",
    "    return degree*np.pi/180"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "undefined-brand",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10800, 21600)\n"
     ]
    }
   ],
   "source": [
    "# Import topography data\n",
    "# Select the area you want\n",
    "resolution = 0.0167\n",
    "# resolution = 1\n",
    "\n",
    "lon_area = [-180., 180.]\n",
    "lat_area = [-90., 90.]\n",
    "# Get mesh-shape topography data\n",
    "lon_topo, lat_topo, topo = Etopo(lon_area, lat_area, resolution)\n",
    "lon_topo = degree2radians(lon_topo)\n",
    "lat_topo = degree2radians(lat_topo)\n",
    "print(np.shape(lon_topo))\n",
    "# del(lon_topo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "wrapped-nature",
   "metadata": {},
   "outputs": [],
   "source": [
    "#The Course graining part\n",
    "N = 8\n",
    "def rebin(a, shape):\n",
    "    sh = shape[0],a.shape[0]//shape[0],shape[1],a.shape[1]//shape[1]\n",
    "    return a.reshape(sh).mean(-1).mean(1)\n",
    "\n",
    "Width = int(10800/N)\n",
    "Length = int(21600/N)\n",
    "topo = rebin(topo,(Width, Length))\n",
    "lat_topo = rebin(lat_topo,(Width, Length))\n",
    "lon_topo = rebin(lon_topo,(Width, Length))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "british-flush",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1350, 2700)\n",
      "3645000\n",
      "540875\n"
     ]
    }
   ],
   "source": [
    "#extracting the unique elevations\n",
    "hieght = np.sort(topo.flatten())\n",
    "uniqe = np.unique(hieght)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "sharing-catholic",
   "metadata": {},
   "outputs": [],
   "source": [
    "#sampling the elevations\n",
    "sampledata = np.linspace(0, len(uniqe)-1, num = 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "global-poetry",
   "metadata": {},
   "outputs": [],
   "source": [
    "#this function calculates the radius of gyration for a 2D array\n",
    "def radiusofgyration(m,lw):\n",
    "    labelList = arange(lw.max() + 1)\n",
    "    area = measurements.sum(m, lw, labelList)\n",
    "    cm = measurements.center_of_mass(m, lw, labelList)\n",
    "    nx = shape(lw)[0]\n",
    "    ny = shape(lw)[1]\n",
    "    rad2 = zeros(int(lw.max()+1))\n",
    "    for ix in range(nx):\n",
    "        for iy in range(ny):\n",
    "            ilw = lw[ix,iy];\n",
    "            if (ilw>0):\n",
    "                dr = array([ix,iy])-cm[ilw]\n",
    "                dr2 = dot(dr,dr)\n",
    "                rad2[ilw] = rad2[ilw] + dr2\n",
    "    \n",
    "    rad = rad2/area\n",
    "    area = area[area != 0]\n",
    "    rad = rad[np.logical_not(np.isnan(rad))] \n",
    "    return rad, area"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "quantitative-forwarding",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-37-c948fab60a1f>:16: RuntimeWarning: invalid value encountered in true_divide\n",
      "  rad = rad2/area\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
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    }
   ],
   "source": [
    "#the major part of the code where we calculate the mean cluster size and the correlation length for different elevations\n",
    "kesi = []\n",
    "meaniland = []\n",
    "sample_uniqe = []\n",
    "k = 0\n",
    "for i in (sampledata):\n",
    "    print(k)\n",
    "    sample_uniqe.append(uniqe[int(i)])\n",
    "    hieght_array = (topo[:,:] <= uniqe[int(i)])\n",
    "    lw, num = measurements.label(hieght_array)\n",
    "    for l in range(len(lw)):\n",
    "                if(lw[l][0] != 0 and lw[l][-1] != 0 and lw[l][-1] != lw[l][0]):\n",
    "                    lw[lw == lw[l][0]] = lw[l][-1]\n",
    "    \n",
    "    gyration, area = radiusofgyration(hieght_array,lw)\n",
    "    index = np.argmax(area)\n",
    "    area = np.delete(area, index)\n",
    "    gyration = np.delete(gyration, index)\n",
    "    meaniland.append(np.mean(area))\n",
    "    kesi.append(np.mean(gyration*area)/np.mean(area))\n",
    "    k = k+1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "surgical-hungary",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2c91d16ee0>]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#ploting the correlation length\n",
    "plot(sample_uniqe, kesi, \".-\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "significant-consolidation",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2c91fa4400>]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#ploting the mean cluster size\n",
    "plot(sample_uniqe, meaniland,\".-\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "agreed-conversation",
   "metadata": {},
   "outputs": [],
   "source": [
    "from haversine import haversine, Unit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "wrapped-bulletin",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "unnecessary-bulgarian",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "rapid-hours",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "language_info": {
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