add teaching materials (#54)

teaching_material/Assignment/Preparatory_exercises/A01_Q1.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "0172ff30-bee8-4cc9-8146-97d65e5289fb",
+   "metadata": {},
+   "source": [
+    "### Python Assignment 1\n",
+    "\n",
+    "In this assignment you will get familiar with analyzing drifter data. The drifters that we will use were released during the Australasian Antarctic Expedition in December 2013, a project designed to characterize eddy dispersion and diffusivity along an Antarctic Circumpolar Current front. For more information you may take a look at [this scientific article](https://doi.org/10.1002/2015JC010972). An animation of the drifters can be found on http://oceanparcels.org/aaemap.\n",
+    "\n",
+    "We assume that you have completed all steps in the *Getting python-ready for Dynamical Oceanography* document and have a new environment called *dyoc*. Now check that you are in the right environment by running the following cell:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9256daff-3fdd-4893-aced-382f93bbb794",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "!conda env list"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "99ea69f2-3199-4a7d-b4e2-0d4bce78c7f0",
+   "metadata": {},
+   "source": [
+    "You should see an asterisk next to your *dyoc* environment. If this is not the case, you may stop the *Jupyter lab* instance using `ctrl + c` in your terminal (Mac) or Anaconda prompt (Windows). Then type `conda activate dyoc` to activate the environment and `jupyter lab` to start *Jupyter lab* again.  \n",
+    "\n",
+    "Now import the following packages:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "09816b5e-3c73-48fa-98fa-81f2766743cf",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import json\n",
+    "import matplotlib.pyplot as plt\n",
+    "import matplotlib.dates as mdates\n",
+    "import matplotlib.colors as mcolors\n",
+    "import matplotlib.cm\n",
+    "import cartopy\n",
+    "import cmocean\n",
+    "import geopy.distance"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "257c5e38-a90c-49f2-bb2c-73b175d15b45",
+   "metadata": {},
+   "source": [
+    "Then download the file `aaedrifters.json` from http://oceanparcels.org/aaemap by clicking on the right-most of the four icons on the bottom-left. Put that file it in the same directory or folder as this notebook and load the data using the code below"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "06e5f44e-7570-4e10-9d13-96a88b173a4e",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "def reshape_jsonarrays(item):\n",
+    "    time = np.array([d[0] for d in item[1]], dtype='datetime64')\n",
+    "    lat = np.array([d[1] for d in item[1]], dtype='float')\n",
+    "    lon = np.array([d[2] for d in item[1]], dtype='float')\n",
+    "    return {'name':item[0], 'time':time, 'lat':lat, 'lon':lon}\n",
+    "\n",
+    "with open(\"aaedrifters.json\") as fp:\n",
+    "    jsondata = json.load(fp)\n",
+    "\n",
+    "drifters = [reshape_jsonarrays(item) for item in jsondata.items()]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7b2fbd30",
+   "metadata": {},
+   "source": [
+    "Have a quick look of the content of the new `drifter` list by running the following cell:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "440cae47",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "drifters"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ee738656-47e6-4a19-9dcc-700c555f6a33",
+   "metadata": {},
+   "source": [
+    "The drifter pairs were deployed on a straight line along the cruise track between approximately (56.0°S, 157.2°E) and (58.8°S, 153.5°E) over a 25 h period starting on 11 December 2013.  \n",
+    "\n",
+    "Make a simple plot of all trajectories in `drifters` using `plt.plot`, both for the complete duration of the experiment and the first ten days after release."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c5342e54-a195-4883-80ce-5c265ab9069f",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6ce3b0b6-7469-41b2-9fcf-3b62d462d27e",
+   "metadata": {},
+   "source": [
+    "To get a better view on the trajectories, it might be nice to show the continents as well. For this we use the `cartopy` package. Now run the following cell and see the resulting map."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9de0bef7-36ae-4cc3-b025-bb1dcf89c242",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "# We use the Platecarree projection centered at 180 degrees longitude\n",
+    "# on Cartopy's website you can find other projections to play around with\n",
+    "projection = cartopy.crs.PlateCarree(central_longitude=180)\n",
+    "\n",
+    "# whenever adding data having latitude-longitude coordinates, use PlateCarree() as coordinate reference system\n",
+    "data_crs = cartopy.crs.PlateCarree()\n",
+    "\n",
+    "# initialisation of the figure\n",
+    "fig = plt.figure(figsize=(12, 5))\n",
+    "ax = fig.add_subplot(1, 1, 1, projection=projection)\n",
+    "\n",
+    "# plot coastlines and colour the land surfaces\n",
+    "ax.coastlines(resolution='50m')\n",
+    "ax.add_feature(cartopy.feature.LAND)\n",
+    "\n",
+    "# plot trajectories\n",
+    "for d in drifters[:]:\n",
+    "    ax.plot(d['lon'], d['lat'], transform=data_crs, lw=0.8)\n",
+    "\n",
+    "# plot grid lines and format the labels\n",
+    "# xlocs is needed because the locator does not work so well when crossing 180 degrees longitude\n",
+    "gl = ax.gridlines(crs=data_crs, draw_labels=['bottom','left'], linewidth=0.5,\n",
+    "              color='gray', alpha=0.5, linestyle='--', xlocs=range(-180,181,10))\n",
+    "gl.xformatter = cartopy.mpl.gridliner.LONGITUDE_FORMATTER\n",
+    "gl.yformatter = cartopy.mpl.gridliner.LATITUDE_FORMATTER\n",
+    "\n",
+    "# zoom out to see more land masses\n",
+    "ax.set_extent((142,228,-77,-32), crs=data_crs)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ccc5136f-377d-408d-a7c3-02254c2757e5",
+   "metadata": {},
+   "source": [
+    "Complete the function `drifter_velocity` below that computes the zonal and meridional velocities of a drifter. The function takes an element of `drifters` as an argument and returns two arrays, `u` and `v`. The remaining code will plot your results for drifter 130263. Make sure the vectors are aligned with the trajectory."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a605b9eb-6774-43cb-9a19-9bd8cd5f90a3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ANSWER\n",
+    "def drifter_velocity(data):\n",
+    "    \"\"\"compute zonal and meridional velocities of drifter\n",
+    "    data : dictionary containing arrays time, lat and lon\n",
+    "    u, v : array, zonal (meridional) velocity\n",
+    "    \"\"\"\n",
+    "    # enter your code here\n",
+    "    return u,v\n",
+    "\n",
+    "data = drifters[4]\n",
+    "u,v = drifter_velocity(data)\n",
+    "\n",
+    "crs = cartopy.crs.PlateCarree()\n",
+    "ax = plt.axes(projection=crs)\n",
+    "pids = slice(1200,1550,4)\n",
+    "Q = ax.quiver(data['lon'][pids], data['lat'][pids], u[pids], v[pids], transform=crs, lw=0.5)\n",
+    "ax.quiverkey(Q, 0.92, 0.05, 0.5, label='0.5 m/s')\n",
+    "ax.set_title(f\"velocity of drifter {data['name']}\")\n",
+    "ax.gridlines(draw_labels=['left','bottom'], dms=True)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ad1b4032-437a-4797-9502-bb98e6e04409",
+   "metadata": {},
+   "source": [
+    "Now use the function `drifter_velocity` to create maps of zonal and meridional velocity for all drifters. Part of the code to plot the results has been given below.  \n",
+    "Hint: use `ax.scatter` to change colour along the trajectories."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "dc3be3f1-312f-472e-89b1-1d3a8d390cb3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# compute velocities here"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ac2f5a0d-7030-451f-91ef-9086075aa824",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ax = plt.axes(projection=cartopy.crs.PlateCarree(central_longitude=180))\n",
+    "\n",
+    "# plot results for u here\n",
+    "\n",
+    "ax.set_title(\"zonal velocity\")\n",
+    "ax.coastlines('50m')\n",
+    "ax.gridlines(draw_labels=['left','bottom'], transform=cartopy.crs.PlateCarree(), xlocs=range(-180,180,10))\n",
+    "ax.figure.colorbar(p, orientation='horizontal', extend='both', label=\"u (m/s)\", aspect=50, pad=0.08)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a7c7cfff-00de-4883-9e3c-a2ca77702ae0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ax = plt.axes(projection=cartopy.crs.PlateCarree(central_longitude=180))\n",
+    "\n",
+    "# plot results for v here\n",
+    "\n",
+    "ax.set_title(\"meridional velocity\")\n",
+    "ax.coastlines('50m')\n",
+    "ax.gridlines(draw_labels=['left','bottom'], transform=cartopy.crs.PlateCarree(), xlocs=range(-180,180,10))\n",
+    "ax.figure.colorbar(p, orientation='horizontal', extend='both', label=\"v (m/s)\", aspect=50, pad=0.08)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "26b13693-4587-4d8a-9126-a24fe3146d4e",
+   "metadata": {},
+   "source": [
+    "The drifters have been released in pairs, about 13 meter apart on either side of the ship. This makes it possible to analyze the separation distance, which is a measure for dispersion. The cell below creates a list, `dists`, of dictionaries containing time, launching latitude, names and distance, $D$, between the drifters of each pair.  \n",
+    "Run it now and plot the drifter separation as a function of time for all drifters for the first ten days after launch. You may change the scale of the y-axis to logarithmic or symmetric logarithmic with `ax.set_yscale`. How does the separation after ten days depend on launching latitude?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "366a3e9c-14df-44b4-b8f2-25ce1ca75a16",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def separation(data1, data2):\n",
+    "    \"\"\"calculate separation distance between two drifters\"\"\"\n",
+    "    time1 = data1['time']\n",
+    "    time2 = data2['time']\n",
+    "    time = np.array(sorted(set(time1).intersection(set(time2))))\n",
+    "    tids1 = np.searchsorted(time1, time)\n",
+    "    tids2 = np.searchsorted(time2, time)\n",
+    "    lats1 = data1['lat'][tids1]\n",
+    "    lons1 = data1['lon'][tids1]\n",
+    "    lats2 = data2['lat'][tids2]\n",
+    "    lons2 = data2['lon'][tids2]\n",
+    "    dist = [geopy.distance.distance((lat1,lon1),(lat2,lon2)).m for (lat1, lon1, lat2, lon2)\n",
+    "            in zip(lats1, lons1, lats2, lons2)]\n",
+    "    return {'name1':data1['name'], 'name2':data2['name'], 'time':time,\n",
+    "            'lat0':data1['lat'][0], 'distance':np.array(dist)}\n",
+    "\n",
+    "lats = np.array([d['lat'][0] for d in drifters])\n",
+    "pairids = lats.argsort().reshape((-1,2)).tolist()\n",
+    "dists = []\n",
+    "for n,(i,j) in enumerate(pairids):\n",
+    "    print(f\"\\ranalyzing pair {n+1}/{len(pairids)}\", end=\"\")\n",
+    "    dists.append(separation(drifters[i], drifters[j]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8416d797-094b-480c-b7dc-a1d1a2ec0b8d",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "840a24d2-b388-4489-ad0d-e478cefe3a91",
+   "metadata": {},
+   "source": [
+    "It is time to compare your results. Create a plot of the pairwise dispersion, $D^2$, similar to figure 5a in the [article](https://doi.org/10.1002/2015JC010972). You do not need to fit the data and calculate the slopes, but do check if the impact of the outlier drifter pair on the mean is similar."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ba5fe542-78fa-48f6-8ac9-baf9d276143e",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.1"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}