parcels/examples/tutorial_SummedFields.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tutorial on how to combine different Fields for advection into a `SummedField` object"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In some oceanographic applications, you may want to advect particles using a combination of different velocity data sets. For example, particles at the surface are transported by a combination of geostrophic, Ekman and Stokes flow. And often, these flows are not even on the same grid.\n",
    "\n",
    "One option would be to write a  `Kernel` that computes the movement of particles due to each of these flows. However, in Parcels it is possible to directly combine different flows (without interpolation) and feed them into the built-in `AdvectionRK4` kernel. For that, we use so-called `SummedField` objects.\n",
    "\n",
    "This tutorial shows how to use these `SummedField` with a very idealised example. We start by importing the relevant modules."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from parcels import Field, FieldSet, ParticleSet, JITParticle, plotTrajectoriesFile, AdvectionRK4\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's first define a zonal and meridional velocity field on a 1kmx1km grid with a flat mesh. The zonal velocity is uniform and 1 m/s, and the meridional velocity is zero everywhere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "xdim, ydim = (10, 20)\n",
    "Uflow = Field('U', np.ones((ydim, xdim), dtype=np.float32),\n",
    "              lon=np.linspace(0., 1e3, xdim, dtype=np.float32),\n",
    "              lat=np.linspace(0., 1e3, ydim, dtype=np.float32))\n",
    "Vflow = Field('V', np.zeros((ydim, xdim), dtype=np.float32), grid=Uflow.grid)\n",
    "fieldset_flow = FieldSet(Uflow, Vflow)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then run a particle and plot its trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: Compiled JITParticleAdvectionRK4 ==> /var/folders/r2/8593q8z93kd7t4j9kbb_f7p00000gn/T/parcels-501/f4a8b4db3aa8d583976f0284a7a13f1c.so\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11041fa90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pset = ParticleSet(fieldset_flow, pclass=JITParticle, lon=[0], lat=[900])\n",
    "output_file = pset.ParticleFile(name='SummedFieldParticle_flow.nc', outputdt=1)\n",
    "pset.execute(AdvectionRK4, runtime=10, dt=1, output_file=output_file)\n",
    "output_file.export()  # export the trajectory data to a netcdf file\n",
    "plotTrajectoriesFile('SummedFieldParticle_flow.nc');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The trajectory plot shows a particle moving eastward on the 1 m/s flow, as expected"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's define another set of velocities (`Ustokes, Vstokes`) on a different, higher-resolution grid. This flow is southward at -0.2 m/s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "gf = 10  # factor by which the resolution of this grid is higher than of the original one.\n",
    "Ustokes = Field('U', np.zeros((ydim*gf, xdim*gf), dtype=np.float32),\n",
    "                lon=np.linspace(0., 1e3, xdim*gf, dtype=np.float32),\n",
    "                lat=np.linspace(0., 1e3, ydim*gf, dtype=np.float32))\n",
    "Vstokes = Field('V', -0.2*np.ones((ydim*gf, xdim*gf), dtype=np.float32), grid=Ustokes.grid)\n",
    "fieldset_stokes=FieldSet(Ustokes, Vstokes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We run a particle in this `FieldSet` and also plot its trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: Compiled JITParticleAdvectionRK4 ==> /var/folders/r2/8593q8z93kd7t4j9kbb_f7p00000gn/T/parcels-501/4d88daba7f9f4523f96fbc7c30b967ee.so\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1131bf2d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pset = ParticleSet(fieldset_stokes, pclass=JITParticle, lon=[0], lat=[900])\n",
    "output_file = pset.ParticleFile(name='SummedFieldParticle_stokes.nc', outputdt=1)\n",
    "pset.execute(AdvectionRK4, runtime=10, dt=1, output_file=output_file)\n",
    "output_file.export()  # export the trajectory data to a netcdf file\n",
    "plotTrajectoriesFile('SummedFieldParticle_stokes.nc');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now comes the trick of the `SummedFields`. We can simply define a new `FieldSet` with a summation of different `Fields`, as in `U=fieldset_flow.U+fieldset_stokes.U`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "fieldset_sum = FieldSet(U=fieldset_flow.U+fieldset_stokes.U, V=fieldset_flow.V+fieldset_stokes.V)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And if we then run the particle again and plot its trajectory, we see that it moves southeastward!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: Compiled JITParticleAdvectionRK4 ==> /var/folders/r2/8593q8z93kd7t4j9kbb_f7p00000gn/T/parcels-501/b144599600769c9fe6b24339a7949645.so\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108165890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pset = ParticleSet(fieldset_sum, pclass=JITParticle, lon=[0], lat=[900])\n",
    "output_file = pset.ParticleFile(name='SummedFieldParticle_sum.nc', outputdt=1)\n",
    "pset.execute(AdvectionRK4, runtime=10, dt=1, output_file=output_file)\n",
    "output_file.export()  # export the trajectory data to a netcdf file\n",
    "plotTrajectoriesFile('SummedFieldParticle_sum.nc');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What happens under the hood is that each `Field` in the `SummedField` is interpolated separately to the particle location, and that the different velocities are added in each step of the RK4 advection. So `SummedFields` are effortless to users.\n",
    "\n",
    "Note that `SummedFields` work for any type of `Field`, not only for velocities. Any call to a `Field` interpolation (`fieldset.fld[time, lon, lat, depth]`) will return the sum of all `Fields` in the list if `fld` is a `SummedField`."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}