{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tutorial on Units and UnitConverters in Parcels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In most applications, Parcels works with  `spherical` meshes, where longitude and latitude are given in degrees, while depth is given in meters. But it is also possible to use `flat` meshes, where longitude and latitude are given in meters (note that the dimensions are then still called `longitude` and `latitude` for consistency reasons).\n",
    "\n",
    "In all cases, velocities are given in m/s. So Parcels seemlessly converts between meters and degrees, under the hood. For transparency, this tutorial explain how this works."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's first import the relevant modules, and create dictionaries for the `U`, `V` and `temp` data arrays, with the velocities 1 m/s and the temperature 20C. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from parcels import Field, FieldSet\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "xdim, ydim = (10, 20)\n",
    "data = {'U': np.ones((ydim, xdim), dtype=np.float32), \n",
    "        'V': np.ones((ydim, xdim), dtype=np.float32),\n",
    "        'temp': 20*np.ones((ydim, xdim), dtype=np.float32)}\n",
    "dims = {'lon': np.linspace(-15, 5, xdim, dtype=np.float32),\n",
    "        'lat': np.linspace(35, 60, ydim, dtype=np.float32)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can convert these data and dims to a FieldSet object using `FieldSet.from_data`. We add the argument `mesh='spherical'` (this is the default option) to signal that all longitudes and latitudes are in degrees. \n",
    "\n",
    "Plotting the `U` field indeed shows a uniform 1m/s eastward flow. The `.show()` method recognises that this is a spherical mesh and hence plots the northwest European coastlines on top."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x311950810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fieldset = FieldSet.from_data(data, dims, mesh='spherical')\n",
    "fieldset.U.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, printing the velocites directly shows something perhaps surprising. Here, we use the square-bracket field-interpolation notation to print the field value at (5W, 40N, 0m depth) at time 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1.1747725785927632e-05, 8.999280057595393e-06, 20.0)\n"
     ]
    }
   ],
   "source": [
    "print((fieldset.U[0, 0, 40, -5], fieldset.V[0, 0, 40, -5], fieldset.temp[0, 0, 40, -5]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the temperature field indeed is 20C, as we defined, these printed velocities are much smaller. \n",
    "\n",
    "This is because Parcels converts under the hood from m/s to degrees/s. This conversion is done with a `UnitConverter` object, which is stored in the `.units` attribute of each Field. Below, we print these"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U: <parcels.tools.converters.GeographicPolar object at 0x10b550050>\n",
      "V: <parcels.tools.converters.Geographic object at 0x10b550090>\n",
      "temp: <parcels.tools.converters.UnitConverter object at 0x311357810>\n"
     ]
    }
   ],
   "source": [
    "for fld in [fieldset.U, fieldset.V, fieldset.temp]:\n",
    "    print('%s: %s' % (fld.name, fld.units))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the U field has a `GeographicPolar` UnitConverter object, the V field has a `Geographic` Unitconverter and the `temp` field has a `UnitConverter` object. \n",
    "\n",
    "Indeed, if we multiply the value of the V field with 1852 * 60 (the number of meters in 1 degree of latitude), we get the expected 1 m/s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0000000000000002\n"
     ]
    }
   ],
   "source": [
    "print(fieldset.V[0, 0, 40, -5]* 1852*60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that you can also interpolate the Field without a unit conversion, by using the `eval()` method and setting `applyConversion=False`, as below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "print(fieldset.V.eval(0, 0, 40, -5, applyConversion=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### UnitConverters for `mesh='flat'`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If longitudes and latitudes are given in meters, rather than degrees, simply add `mesh='flat'` when creating the FieldSet object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1e5d1850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U: 1.000000 <parcels.tools.converters.UnitConverter object at 0x1a1e614450>\n",
      "V: 1.000000 <parcels.tools.converters.UnitConverter object at 0x1a1e6145d0>\n",
      "temp: 20.000000 <parcels.tools.converters.UnitConverter object at 0x1091cefd0>\n"
     ]
    }
   ],
   "source": [
    "fieldset_flat = FieldSet.from_data(data, dims, mesh='flat')\n",
    "fieldset_flat.U.show()\n",
    "for fld in [fieldset_flat.U, fieldset_flat.V, fieldset_flat.temp]:\n",
    "    print('%s: %f %s' % (fld.name, fld[0, 0, 40, -5], fld.units))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, in this case all Fields have the same default `UnitConverter` object. Note that the coastlines have also gone in the plot, as `.show()` recognises that this is a flat mesh."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### UnitConverters for Diffusion fields"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The units for Brownian diffusion are in $m^2/s$. If (and only if!) the diffusion fields are called `kh_zonal` and `kh_meridional`, Parcels will automatically assign the correct Unitconverter objects to these fields."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kh_zonal: 1.380091e-08 <parcels.tools.converters.GeographicPolarSquare object at 0x10b5500d0>\n",
      "Kh_meridional: 8.098704e-09 <parcels.tools.converters.GeographicSquare object at 0x10b550110>\n"
     ]
    }
   ],
   "source": [
    "kh_zonal = 100  # in m^2/s\n",
    "kh_meridional = 100  # in m^2/s\n",
    "\n",
    "fieldset.add_field(Field('Kh_zonal', kh_zonal*np.ones((ydim, xdim), dtype=np.float32), grid=fieldset.U.grid))\n",
    "fieldset.add_field(Field('Kh_meridional', kh_meridional*np.ones((ydim, xdim), dtype=np.float32), grid=fieldset.U.grid))\n",
    "\n",
    "for fld in [fieldset.Kh_zonal, fieldset.Kh_meridional]:\n",
    "    print('%s: %e %s' % (fld.name, fld[0, 0, 40, -5], fld.units))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, the unitconverters are `GeographicPolarSquare` and `GeographicSquare`, respectively.\n",
    "\n",
    "Indeed, multiplying with $(1852\\cdot60)^2$ returns the original value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100.0\n"
     ]
    }
   ],
   "source": [
    "deg_to_m = 1852*60\n",
    "print(fieldset.Kh_meridional[0, 0, 40, -5]*deg_to_m**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding a UnitConverter object to a Field"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, to summarise, here is a table with all the conversions\n",
    "\n",
    "| Field name | Converter object | Conversion for `mesh='spherical'`| Conversion for `mesh='flat'`|\n",
    "|-------|-----------------|-----------------------------------|\n",
    "| 'U' | `GeographicPolar`| $1852 \\cdot 60 \\cdot \\cos(lat \\cdot \\frac{\\pi}{180})$ | 1 |\n",
    "| 'V' | `Geographic` | $1852 \\cdot 60 $ | 1 |\n",
    "| 'Kh_zonal' | `GeographicPolarSquare` | $(1852 \\cdot 60 \\cdot \\cos(lat \\cdot \\frac{\\pi}{180}))^2$ | 1 |\n",
    "| 'Kh_meridional' | `GeographicSquare` | $(1852 \\cdot 60)^2 $ | 1 |\n",
    "| All other fields | `UnitConverter` | 1 | 1 |\n",
    "\n",
    "Only four Field names are recognised and assigned an automatic UnitConverter object. This means that things might go very wrong when e.g. a velocity field is not called `U` or `V`. \n",
    "\n",
    "Fortunately, you can always add a UnitConverter later, as explained below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "fieldset.add_field(Field('Ustokes', np.ones((ydim, xdim), dtype=np.float32), grid=fieldset.U.grid))\n",
    "print(fieldset.Ustokes[0, 0, 40, -5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This value for `Ustokes` of course is not as expected, since the mesh is spherical and hence this would mean 1 degree/s velocity. Assigning the correct `GeographicPolar` Unitconverter gives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1747725785927632e-05\n",
      "0.9999999999999999\n"
     ]
    }
   ],
   "source": [
    "from parcels.tools.converters import GeographicPolar \n",
    "\n",
    "fieldset.Ustokes.units = GeographicPolar()\n",
    "print(fieldset.Ustokes[0, 0, 40, -5])\n",
    "print(fieldset.Ustokes[0, 0, 40, -5]*1852*60*np.cos(40*np.pi/180))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, the UnitConverter can be set when the `FieldSet` or `Field` is created by using the `fieldtype` argument (use a dictionary in the case of `FieldSet` construction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1747725785927632e-05\n"
     ]
    }
   ],
   "source": [
    "fieldset.add_field(Field('Ustokes2', np.ones((ydim, xdim), dtype=np.float32), grid=fieldset.U.grid, fieldtype='U'))\n",
    "print(fieldset.Ustokes2[0, 0, 40, -5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using velocities in units other than m/s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some OGCM store velocity data in units of e.g. cm/s. For these cases, Field objects have a method `set_scaling_factor()`. \n",
    "\n",
    "If your data is in cm/s and if you want to use the built-in Advection kernels, you will therefore have to use `fieldset.U.set_scaling_factor(100)` and `fieldset.V.set_scaling_factor(100)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "fieldset.add_field(Field('Ucm', 0.01*np.ones((ydim, xdim), dtype=np.float32), grid=fieldset.U.grid))\n",
    "fieldset.Ucm.set_scaling_factor(100)\n",
    "print(fieldset.Ucm[0, 0, 40, -5])"
   ]
  }
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