{ "cells": [ { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n# FSLE experiment in med\n\nExample to build Finite Size Lyapunov Exponents, parameter values must be adapted for your case.\n\nExample use a method similar to `AVISO flse`_\n\n https://www.aviso.altimetry.fr/en/data/products/value-added-products/\n fsle-finite-size-lyapunov-exponents/fsle-description.html\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from matplotlib import pyplot as plt\nfrom numba import njit\nfrom numpy import arange, arctan2, empty, isnan, log, ma, meshgrid, ones, pi, zeros\n\nfrom py_eddy_tracker import start_logger\nfrom py_eddy_tracker.data import get_demo_path\nfrom py_eddy_tracker.dataset.grid import GridCollection, RegularGridDataset\n\nstart_logger().setLevel(\"ERROR\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ADT in med\n:py:meth:`~py_eddy_tracker.dataset.grid.GridCollection.from_netcdf_cube` method is\nmade for data stores in time cube, you could use also\n:py:meth:`~py_eddy_tracker.dataset.grid.GridCollection.from_netcdf_list` method to\nload data-cube from multiple file.\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "c = GridCollection.from_netcdf_cube(\n get_demo_path(\"dt_med_allsat_phy_l4_2005T2.nc\"),\n \"longitude\",\n \"latitude\",\n \"time\",\n # To create U/V variable\n heigth=\"adt\",\n)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Methods to compute FSLE\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "@njit(cache=True, fastmath=True)\ndef check_p(x, y, flse, theta, m_set, m, dt, dist_init=0.02, dist_max=0.6):\n \"\"\"\n Check if distance between eastern or northern particle to center particle is bigger than `dist_max`\n \"\"\"\n nb_p = x.shape[0] // 3\n delta = dist_max**2\n for i in range(nb_p):\n i0 = i * 3\n i_n = i0 + 1\n i_e = i0 + 2\n # If particle already set, we skip\n if m[i0] or m[i_n] or m[i_e]:\n continue\n # Distance with north\n dxn, dyn = x[i0] - x[i_n], y[i0] - y[i_n]\n dn = dxn**2 + dyn**2\n # Distance with east\n dxe, dye = x[i0] - x[i_e], y[i0] - y[i_e]\n de = dxe**2 + dye**2\n\n if dn >= delta or de >= delta:\n s1 = dn + de\n at1 = 2 * (dxe * dxn + dye * dyn)\n at2 = de - dn\n s2 = ((dxn + dye) ** 2 + (dxe - dyn) ** 2) * (\n (dxn - dye) ** 2 + (dxe + dyn) ** 2\n )\n flse[i] = 1 / (2 * dt) * log(1 / (2 * dist_init**2) * (s1 + s2**0.5))\n theta[i] = arctan2(at1, at2 + s2) * 180 / pi\n # To know where value are set\n m_set[i] = False\n # To stop particle advection\n m[i0], m[i_n], m[i_e] = True, True, True\n\n\n@njit(cache=True)\ndef build_triplet(x, y, step=0.02):\n \"\"\"\n Triplet building for each position we add east and north point with defined step\n \"\"\"\n nb_x = x.shape[0]\n x_ = empty(nb_x * 3, dtype=x.dtype)\n y_ = empty(nb_x * 3, dtype=y.dtype)\n for i in range(nb_x):\n i0 = i * 3\n i_n, i_e = i0 + 1, i0 + 2\n x__, y__ = x[i], y[i]\n x_[i0], y_[i0] = x__, y__\n x_[i_n], y_[i_n] = x__, y__ + step\n x_[i_e], y_[i_e] = x__ + step, y__\n return x_, y_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Settings\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Step in degrees for ouput\nstep_grid_out = 1 / 25.0\n# Initial separation in degrees\ndist_init = 1 / 50.0\n# Final separation in degrees\ndist_max = 1 / 5.0\n# Time of start\nt0 = 20268\n# Number of time step by days\ntime_step_by_days = 5\n# Maximal time of advection\n# Here we limit because our data cube cover only 3 month\nnb_days = 85\n# Backward or forward\nbackward = True" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Particles\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "x0_, y0_ = -5, 30\nlon_p = arange(x0_, x0_ + 43, step_grid_out)\nlat_p = arange(y0_, y0_ + 16, step_grid_out)\ny0, x0 = meshgrid(lat_p, lon_p)\ngrid_shape = x0.shape\nx0, y0 = x0.reshape(-1), y0.reshape(-1)\n# Identify all particle not on land\nm = ~isnan(c[t0].interp(\"adt\", x0, y0))\nx0, y0 = x0[m], y0[m]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## FSLE\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Array to compute fsle\nfsle = zeros(x0.shape[0], dtype=\"f4\")\ntheta = zeros(x0.shape[0], dtype=\"f4\")\nmask = ones(x0.shape[0], dtype=\"f4\")\nx, y = build_triplet(x0, y0, dist_init)\nused = zeros(x.shape[0], dtype=\"bool\")\n\n# advection generator\nkw = dict(t_init=t0, nb_step=1, backward=backward, mask_particule=used, u_name=\"u\", v_name=\"v\")\np = c.advect(x, y, time_step=86400 / time_step_by_days, **kw)\n\n# We check at each step of advection if particle distance is over `dist_max`\nfor i in range(time_step_by_days * nb_days):\n t, xt, yt = p.__next__()\n dt = t / 86400.0 - t0\n check_p(xt, yt, fsle, theta, mask, used, dt, dist_max=dist_max, dist_init=dist_init)\n\n# Get index with original_position\ni = ((x0 - x0_) / step_grid_out).astype(\"i4\")\nj = ((y0 - y0_) / step_grid_out).astype(\"i4\")\nfsle_ = empty(grid_shape, dtype=\"f4\")\ntheta_ = empty(grid_shape, dtype=\"f4\")\nmask_ = ones(grid_shape, dtype=\"bool\")\nfsle_[i, j] = fsle\ntheta_[i, j] = theta\nmask_[i, j] = mask\n# Create a grid object\nfsle_custom = RegularGridDataset.with_array(\n coordinates=(\"lon\", \"lat\"),\n datas=dict(\n fsle=ma.array(fsle_, mask=mask_),\n theta=ma.array(theta_, mask=mask_),\n lon=lon_p,\n lat=lat_p,\n ),\n centered=True,\n)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Display FSLE\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig = plt.figure(figsize=(13, 5), dpi=150)\nax = fig.add_axes([0.03, 0.03, 0.90, 0.94])\nax.set_xlim(-6, 36.5), ax.set_ylim(30, 46)\nax.set_aspect(\"equal\")\nax.set_title(\"Finite size lyapunov exponent\", weight=\"bold\")\nkw = dict(cmap=\"viridis_r\", vmin=-20, vmax=0)\nm = fsle_custom.display(ax, 1 / fsle_custom.grid(\"fsle\"), **kw)\nax.grid()\n_ = plt.colorbar(m, cax=fig.add_axes([0.94, 0.05, 0.01, 0.9]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Display Theta\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig = plt.figure(figsize=(13, 5), dpi=150)\nax = fig.add_axes([0.03, 0.03, 0.90, 0.94])\nax.set_xlim(-6, 36.5), ax.set_ylim(30, 46)\nax.set_aspect(\"equal\")\nax.set_title(\"Theta from finite size lyapunov exponent\", weight=\"bold\")\nkw = dict(cmap=\"Spectral_r\", vmin=-180, vmax=180)\nm = fsle_custom.display(ax, fsle_custom.grid(\"theta\"), **kw)\nax.grid()\n_ = plt.colorbar(m, cax=fig.add_axes([0.94, 0.05, 0.01, 0.9]))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.10.6" } }, "nbformat": 4, "nbformat_minor": 0 }