diff --git a/CHANGES.txt b/CHANGES.txt index 1644426..3a1f078 100644 --- a/CHANGES.txt +++ b/CHANGES.txt @@ -8,3 +8,4 @@ v0.7, 4 June 2015 -- Added support for missing values in temperature time seri v0.8, 16 July 2015 -- Added calculations of total MHW days and cumulative intensity v0.9, 14 Sep 2015 -- Added calculation of MHW rank and return period v0.10, 14 Sep 2015 -- Added calculation of normalized MHW intensity +v0.11, 26 Oct 2015 -- Updated documentation diff --git a/build/lib/marineHeatWaves.py b/build/lib/marineHeatWaves.py index f1d7379..9ba4f6b 100644 --- a/build/lib/marineHeatWaves.py +++ b/build/lib/marineHeatWaves.py @@ -101,7 +101,7 @@ def detect(t, temp, climatologyPeriod=[1983,2012], pctile=90, windowHalfWidth=5, Notes: 1. This function assumes that the input time series consist of continuous daily values - with no missing values. Time ranges which start and end part-way through the calendar + with few missing values. Time ranges which start and end part-way through the calendar year are supported. 2. This function supports leap years. This is done by ignoring Feb 29s for the initial @@ -112,9 +112,9 @@ def detect(t, temp, climatologyPeriod=[1983,2012], pctile=90, windowHalfWidth=5, before the start day and ended a half-day after the end-day. (This is consistent with the duration definition as implemented, which assumes duration = end day - start day + 1.) - 4. For the purposes of MHW detection, any missing temp values not interpolated over will be - set equal to the seasonal climatology. This means they will trigger the end/start of any - adjacent temp values which satisfy the MHW criteria. + 4. For the purposes of MHW detection, any missing temp values not interpolated over (through + optional maxPadLLength) will be set equal to the seasonal climatology. This means they will + trigger the end/start of any adjacent temp values which satisfy the MHW criteria. Written by Eric Oliver, Institue for Marine and Antarctic Studies, University of Tasmania, Feb 2015 diff --git a/docs/.ipynb_checkpoints/example_synthetic-checkpoint.ipynb b/docs/.ipynb_checkpoints/example_synthetic-checkpoint.ipynb new file mode 100644 index 0000000..d32c199 --- /dev/null +++ b/docs/.ipynb_checkpoints/example_synthetic-checkpoint.ipynb @@ -0,0 +1,3551 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Marine Heatwaves Definition" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This document describes the `marineHeatWaves` module for python which implements the Marine Heatwave (MHW) definition of Hobday et al. (*manuscript submitted to Progress in Oceanography*). This software is demonstrated by applying the MHW definition to a stochastic red noise process. This was developed as an interactive ipython notebook which the user can run themselves provided they have the required python modules (`numpy`, `scipy`, `datetime`, and `matplotlib`)." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "# Load required modules\n", + "import numpy as np\n", + "from datetime import date\n", + "from matplotlib import pyplot as plt\n", + "%pylab inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Load marineHeatWaves definition module\n", + "import marineHeatWaves as mhw" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Generate synthetic temperature time series" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following code will generate a synthetic daily temperature time series, over the time span 1 Jan 1982 to 31 Dec 2014, using an order-1 autoregressive process." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Generate time vector using datetime format (January 1 of year 1 is day 1)\n", + "t = np.arange(date(1982,1,1).toordinal(),date(2014,12,31).toordinal()+1)\n", + "dates = [date.fromordinal(tt.astype(int)) for tt in t]\n", + "# Generate synthetic temperature time series\n", + "sst = np.zeros(len(t))\n", + "sst[0] = 0 # Initial condition\n", + "a = 0.85 # autoregressive parameter\n", + "for i in range(1,len(t)):\n", + " sst[i] = a*sst[i-1] + 0.75*np.random.randn() + 0.5*np.cos(t[i]*2*np.pi/365.25)\n", + "sst = sst - sst.min() + 5." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Marine Heatwave Detection\n", + "\n", + "The marineHeatWaves (`mhw`) module consists of a number of functions for the detection and characterization of MHWs. The main function is the detection function (`detect`) which takes as input a time series of temperature (and a corresponding time vector) and outputs a set of detected MHWs. We first run the MHW detection algorithm which returns the variable `mhws`, consisting of the detected MHWs, and `clim`, consisting of the climatological (varying by day-of-year) seasonal cycle and extremes threshold:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "mhws, clim = mhw.detect(t, sst)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This algorithm has detected the following number of MHW events:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "65" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mhws['n_events']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first ten events, for example, have the following maximum intensities (in $^\\circ$C):" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[3.3455745852780989,\n", + " 3.5165101781833101,\n", + " 3.5094426025360832,\n", + " 2.8836950818283675,\n", + " 4.5281645612607484,\n", + " 3.6626085409989937,\n", + " 3.1642501721248628,\n", + " 3.0971113963048715,\n", + " 3.5946579814024702,\n", + " 3.1679283319142293]" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mhws['intensity_max'][0:10]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's have a look at some properties of the event with the largest maximum intensity" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Maximum intensity: 4.80172612888 deg. C\n", + "Average intensity: 2.9970910959 deg. C\n", + "Cumulative intensity: 47.9534575345 deg. C-days\n", + "Duration: 16 days\n", + "Start date: 22 November 1989\n", + "End date: 07 December 1989\n" + ] + } + ], + "source": [ + "ev = np.argmax(mhws['intensity_max']) # Find largest event\n", + "print 'Maximum intensity:', mhws['intensity_max'][ev], 'deg. C'\n", + "print 'Average intensity:', mhws['intensity_mean'][ev], 'deg. C'\n", + "print 'Cumulative intensity:', mhws['intensity_cumulative'][ev], 'deg. C-days'\n", + "print 'Duration:', mhws['duration'][ev], 'days'\n", + "print 'Start date:', mhws['date_start'][ev].strftime(\"%d %B %Y\")\n", + "print 'End date:', mhws['date_end'][ev].strftime(\"%d %B %Y\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and a closer look at the identified MHW event:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAA0kAAAJZCAYAAAB82H5vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzsnXecXVW597/P9JlkSuokk0wSAkQCJEjvRRCUooiAXAVs\n", + "qKC+YsEOEsbuVa/1Wq5eryiI9dob6gWliAgqKL0FQnqbSTItk5n1/vGsfc7e+5SZ7L32zJxk/T6f\n", + "ZM7Z+5xnP2etZz3raWstMcbg4eHh4eHh4eHh4eHhoaiaaAY8PDw8PDw8PDw8PDwmE7yT5OHh4eHh\n", + 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"plt.ylim(sst.min()-0.5, sst.max()+0.5)\n", + "plt.ylabel(r'SST [$^\\circ$C]')\n", + "plt.subplot(2,1,2)\n", + "# Find indices for all ten MHWs before and after event of interest and shade accordingly\n", + "for ev0 in np.arange(ev-10, ev+11, 1):\n", + " t1 = np.where(t==mhws['time_start'][ev0])[0][0]\n", + " t2 = np.where(t==mhws['time_end'][ev0])[0][0]\n", + " plt.fill_between(dates[t1:t2+1], sst[t1:t2+1], clim['thresh'][t1:t2+1], \\\n", + " color=(1,0.6,0.5))\n", + "# Find indices for MHW of interest and shade accordingly\n", + "t1 = np.where(t==mhws['time_start'][ev])[0][0]\n", + "t2 = np.where(t==mhws['time_end'][ev])[0][0]\n", + "plt.fill_between(dates[t1:t2+1], sst[t1:t2+1], clim['thresh'][t1:t2+1], \\\n", + " color='r')\n", + "# Plot SST, seasonal cycle, threshold, shade MHWs with main event in red\n", + "plt.plot(dates, sst, 'k-', linewidth=2)\n", + "plt.plot(dates, clim['thresh'], 'g-', linewidth=2)\n", + "plt.plot(dates, clim['seas'], 'b-', linewidth=2)\n", + "plt.title('SST (black), seasonal climatology (blue), \\\n", + " threshold (green), detected MHW events (shading)')\n", + "plt.xlim(mhws['time_start'][ev]-150, mhws['time_end'][ev]+150)\n", + "plt.ylim(clim['seas'].min() - 1, clim['seas'].max() + mhws['intensity_max'][ev] + 0.5)\n", + "plt.ylabel(r'SST [$^\\circ$C]')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Yep, It's certainly picked out the largest event in the series (dark red shading). This event also seems to have been preceded and succeeded by a number of shorter, weaker events (light red shading). Let's have a look at how the MHW statistics are distributed across all the detected events:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAA3UAAAHACAYAAAAFlkHPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xm8JHV97//Xm01UFCTogIrBaDAuY0ATYlwiuP1wATVx\n", + "xQWNUWMSNUZzRW+UyXY15heD3miuCxpEGTUaCOMKUYe4xAUdYBS8xgVFZQYiqyIR4XP/qDrQHM7W\n", + "Z053dXW/no/HeZyq6uqqT/Xp09/+1HdLVSFJkiRJ6qedug5AkiRJkrR6JnWSJEmS1GMmdZIkSZLU\n", + "YyZ1kiRJktRjJnWSJEmS1GMmdZIkSZLUYyZ1Uo8l+UiSZ3QdhyRp9iS5MskBXcfRB0meluTjXceh\n", + "6RXnqZNWJ8n5wO2AnwPXAucC7wLeWiP4x0qyAbhLVZnESZKW1JZR+wG3r6ofDWzfAvwqcEBVfa+j\n", + "8EYqyT8BF1TVq1aw7wY6KFuTXAfctaq+Pc7zanpZUyetXgGPqapbA3cCXgu8HDh+2AMl2WWNY5Mk\n", + 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mhws['duration'][evMax], width=0.6, color=(1,0.5,0.5))\n", + "plt.bar(ev, mhws['duration'][ev], width=0.6, edgecolor=(1,0.,0.), \\\n", + " color='none')\n", + "plt.xlim(0, mhws['n_events'])\n", + "plt.ylabel('[days]')\n", + "plt.title('Duration')\n", + "# Maximum intensity\n", + "plt.subplot(2,2,2)\n", + "evMax = np.argmax(mhws['intensity_max'])\n", + "plt.bar(range(mhws['n_events']), mhws['intensity_max'], width=0.6, \\\n", + " color=(0.7,0.7,0.7))\n", + "plt.bar(evMax, mhws['intensity_max'][evMax], width=0.6, color=(1,0.5,0.5))\n", + "plt.bar(ev, mhws['intensity_max'][ev], width=0.6, edgecolor=(1,0.,0.), \\\n", + " color='none')\n", + "plt.xlim(0, mhws['n_events'])\n", + "plt.ylabel(r'[$^\\circ$C]')\n", + "plt.title('Maximum Intensity')\n", + "# Mean intensity\n", + "plt.subplot(2,2,4)\n", + "evMax = np.argmax(mhws['intensity_mean'])\n", + "plt.bar(range(mhws['n_events']), mhws['intensity_mean'], width=0.6, \\\n", + " color=(0.7,0.7,0.7))\n", + "plt.bar(evMax, mhws['intensity_mean'][evMax], width=0.6, color=(1,0.5,0.5))\n", + "plt.bar(ev, mhws['intensity_mean'][ev], width=0.6, edgecolor=(1,0.,0.), \\\n", + " color='none')\n", + "plt.xlim(0, mhws['n_events'])\n", + "plt.title('Mean Intensity')\n", + "plt.ylabel(r'[$^\\circ$C]')\n", + "plt.xlabel('MHW event number')\n", + "# Cumulative intensity\n", + "plt.subplot(2,2,3)\n", + "evMax = np.argmax(mhws['intensity_cumulative'])\n", + "plt.bar(range(mhws['n_events']), mhws['intensity_cumulative'], width=0.6, \\\n", + " color=(0.7,0.7,0.7))\n", + "plt.bar(evMax, mhws['intensity_cumulative'][evMax], width=0.6, color=(1,0.5,0.5))\n", + "plt.bar(ev, mhws['intensity_cumulative'][ev], width=0.6, edgecolor=(1,0.,0.), \\\n", + " color='none')\n", + "plt.xlim(0, mhws['n_events'])\n", + "plt.title(r'Cumulative Intensity')\n", + "plt.ylabel(r'[$^\\circ$C$\\times$days]')\n", + "plt.xlabel('MHW event number')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The red shaded bars show the largest event on record by duration, maximum intensity, cumulative intensity, and mean intensity, while the red-outlined bars show the specific event chosen above (which happens to be largest by maximum intensity). We can see how this event ranks according to the other metrics as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The 2012 NWA event is ranked number 1 by duration\n", + "The 2012 NWA event is ranked number 1 by maximum intensity\n", + "The 2012 NWA event is ranked number 8 by mean intensity\n", + "The 2012 NWA event is ranked number 1 by cumulative intensity\n" + ] + } + ], + "source": [ + "ranks = mhws['n_events']- np.array(mhws['duration']).argsort().argsort()\n", + "print \"The 2012 NWA event is ranked number \" \\\n", + " + str(ranks[ev]) + \" by duration\"\n", + "ranks = mhws['n_events']- np.array(mhws['intensity_max']).argsort().argsort()\n", + "print \"The 2012 NWA event is ranked number \" \\\n", + " + str(ranks[ev]) + \" by maximum intensity\"\n", + "ranks = mhws['n_events']- np.array(mhws['intensity_mean']).argsort().argsort()\n", + "print \"The 2012 NWA event is ranked number \" \\\n", + " + str(ranks[ev]) + \" by mean intensity\"\n", + "ranks = mhws['n_events']- np.array(mhws['intensity_cumulative']).argsort().argsort()\n", + "print \"The 2012 NWA event is ranked number \" \\\n", + " + str(ranks[ev]) + \" by cumulative intensity\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Block-averaged Marine Heatwave properties" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The marineHeatWaves (`mhw`) module also consists of functions to calculate the average of MHW properties over blocks in time (e.g., annually, decadally). The block-averaging function (`blockAverage`) takes as input a set of detected MHWs (i.e., the output from `detect`, the detection function described above) and outputs the MHW properties averaged over the specified block-length. This output can then be passed through the `meanTrend` function in order to calculate the time-mean and linear trend of the MHW properties over the measurement period.\n", + "\n", + "Let's start by applying the block-averaging function to the Mediterranean MHWs which are stored in the variable `mhws`, using the default block length of 1 year (i.e., annual averages):" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "mhwBlock = mhw.blockAverage(t, mhws)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The variable `mhwBlock` has a set of keys which are time series of the MHW properties over the blocks. The central year of the blocks are stored in the key `years_centre` so we can look at, as an example, time series of MHW counts in each year and the average maximum intensity in each year:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAz8AAAEKCAYAAAA8fet0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XnYJFV5/vHvDcguIKswIAMDRkFBGEDcxx1wjVtcUYyK\n", + "mjiYqDGaX2TiEmOMUUeNEjdEjfu+obgMoKAy7IIIDiD7DgPKIsLz++OcZurt6aW6u6q7ut/7c11z\n", + "zdvV1VWnq7ur6jnLcxQRmJmZmZmZzbp1Jl0AMzMzMzOzcXDwY2ZmZmZm84KDHzMzMzMzmxcc/JiZ\n", + "mZmZ2bzg4MfMzMzMzOYFBz9mZmZmZjYvOPixiZN0tKR3THD/n5Z0g6RfTqoMo5J0t6RdJ10OMzOr\n", + "n6T7SbpFkiZdlnaSvi/pJZMuR5Gkj0r6fxVta5mkz1axLZsMBz+2FkkXS7pa0saFZa+Q9LOadhn5\n", + 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"display_data" + } + ], + "source": [ + "plt.figure(figsize=(14,4))\n", + "plt.subplot(1,2,1)\n", + "plt.plot(mhwBlock['years_centre'], mhwBlock['count'], 'k-o')\n", + "plt.ylim(0,9)\n", + "plt.ylabel('[count]')\n", + "plt.title('Number of MHWs by year')\n", + "plt.subplot(1,2,2)\n", + "plt.plot(mhwBlock['years_centre'], mhwBlock['intensity_max'], 'k-o')\n", + "plt.ylabel(r'[$^\\circ$C]')\n", + "plt.title('Average MHW maximum intensity by year')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can calculate the mean and trend of the MHW properties using the `meanTrend` function:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "There are on average 2.06060606061 MHWs in each year, \n", + " with a linear trend of 0.24064171123 MHW events per decade\n", + "\n", + "The average maximum intensity is 4.03496291446 deg. C, \n", + " with a linear trend of 0.0371253287557 deg. C per decade\n" + ] + } + ], + "source": [ + "mean, trend, dtrend = mhw.meanTrend(mhwBlock)\n", + "print \"There are on average \" + str(mean['count']) + \" MHWs in each year, \\n \\\n", + "with a linear trend of \" + str(10*trend['count']) + \" MHW events per decade\\n\"\n", + "print \"The average maximum intensity is \" + str(mean['intensity_max']) + \" deg. C, \\n \\\n", + "with a linear trend of \" + str(10*trend['intensity_max']) + \" deg. C per decade\"" + ] + } + ], + "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": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/docs/README.txt b/docs/README.txt index 45dac20..81f91d7 100644 --- a/docs/README.txt +++ b/docs/README.txt @@ -8,19 +8,19 @@ Contents ======== - example_bigThreeMHWs.html HTML file of IPython notebook outlining use of - marineHeatWaves code to detect the "big three" - historical marine heatwaves. Original data files - (NOAA OI SST hi-res) not supplied. + marineHeatWaves_manual.html HTML file of IPython notebook outlining use of + marineHeatWaves code to detect the "big three" + historical marine heatwaves. Original data files + (NOAA OI SST hi-res) not supplied due to copyright. - example_synthetic.ipynb IPython notebook outlining use of marineHeatWaves - code to detect events from a synthetic time series. - This notebook can be run by the user as it relies - on internally-generated synthetic temperature data. + example_synthetic.ipynb IPython notebook outlining use of marineHeatWaves + code to detect events from a synthetic time series. + This notebook can be run by the user as it relies only + on internally-generated synthetic temperature data. - example_synthetic.html Static HTML version of example_synthetic.ipynb + example_synthetic.html Static HTML version of example_synthetic.ipynb - README.txt This file + README.txt This file Contact ======= diff --git a/docs/example_bigThreeMHWs.html b/docs/example_bigThreeMHWs.html deleted file mode 100644 index 482f0fd..0000000 --- a/docs/example_bigThreeMHWs.html +++ /dev/null @@ -1,10032 +0,0 @@ - - - - - -MHW - - - - - - - - - - - - - - - - - - - - - - -
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Marine Heatwaves Definition

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This document describes the marineHeatWaves module for python which implements the Marine Heatwave (MHW) definition of Hobday et al. (manuscript in preparation). This software is demonstrated by applying the MHW definition to observed SST records and showing how it identifies three historical MHWs: the 2011 Western Australia event, the 2012 Northwest Atlantic event, and the 2003 Mediterranean event. This was developed as an interactive ipython notebook which the user can run themselves provided they have the required python modules (numpy, scipy, datetime, and matplotlib).

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# Load required modules
-import numpy as np
-from datetime import date
-from matplotlib import pyplot as plt
-%pylab inline
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Populating the interactive namespace from numpy and matplotlib
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# Load marineHeatWaves definition module
-import marineHeatWaves as mhw
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Marine Heatwave Detection

The marineHeatWaves (mhw) module consists of a number of functions for the detection and characterization of MHWs. The main function is the detection function (detect) which takes as input a time series of temperature (and a corresponding time vector) and outputs a set of detected MHWs.

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Case study #1: 2011 Western Australia event

As an example, let's load a daily time series of SST off Western Australia (WA; 112.5$^\circ$E, 29.5$^\circ$S) over the 1982 to 2014 period, remotely-sensed from the AVHRR satellite platform:

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# Load WA SST time series
-sst = np.loadtxt('data/sst_WA.csv', delimiter=',')
-# Generate time vector using datetime format (January 1 of year 1 is day 1)
-t = np.arange(date(1982,1,1).toordinal(),date(2014,12,31).toordinal()+1)
-dates = [date.fromordinal(tt.astype(int)) for tt in t]
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Next we run the MHW detection algorithm which returns the variable mhws, consisting of the detected MHWs, and clim, consisting of the climatological (varying by day-of-year) seasonal cycle and extremes threshold:

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mhws, clim = mhw.detect(t, sst)
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This algorithm has detected the following number of MHW events:

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mhws['n_events']
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The first ten events, for example, have the following maximum intensities (in $^\circ$C):

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mhws['intensity_max'][0:10]
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[2.1493293752236546,
- 1.528071324593725,
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- 1.9655424780608328,
- 2.1381436472234299,
- 2.2683244849783755,
- 1.3314779761042494,
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- 1.4465991856522997]
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Let's have a look at some properties of the event with the largest maximum intensity

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ev = np.argmax(mhws['intensity_max']) # Find largest event
-print 'Maximum intensity:', mhws['intensity_max'][ev], 'deg. C'
-print 'Average intensity:', mhws['intensity_mean'][ev], 'deg. C'
-print 'Cumulative intensity:', mhws['intensity_cumulative'][ev], 'deg. C-days'
-print 'Duration:', mhws['duration'][ev], 'days'
-print 'Start date:', mhws['date_start'][ev].strftime("%d %B %Y")
-print 'End date:', mhws['date_end'][ev].strftime("%d %B %Y")
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Maximum intensity: 6.58207121163 deg. C
-Average intensity: 2.78985968785 deg. C
-Cumulative intensity: 292.935267225 deg. C-days
-Duration: 105 days
-Start date: 24 December 2010
-End date: 07 April 2011
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This turns out to be the infamous 2011 MHW off WA. Let's plot the SST time series over the full record and also have a closer look at the identified MHW event:

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plt.figure(figsize=(14,10))
-plt.subplot(2,1,1)
-# Plot SST, seasonal cycle, and threshold
-plt.plot(dates, sst, 'k-')
-plt.plot(dates, clim['thresh'], 'g-')
-plt.plot(dates, clim['seas'], 'b-')
-plt.title('SST (black), seasonal climatology (blue), \
-          threshold (green), detected MHW events (shading)')
-plt.xlim(t[0], t[-1])
-plt.ylim(sst.min()-0.5, sst.max()+0.5)
-plt.ylabel(r'SST [$^\circ$C]')
-plt.subplot(2,1,2)
-# Find indices for all ten MHWs before and after event of interest and shade accordingly
-for ev0 in np.arange(ev-10, ev+11, 1):
-    t1 = np.where(t==mhws['time_start'][ev0])[0][0]
-    t2 = np.where(t==mhws['time_end'][ev0])[0][0]
-    plt.fill_between(dates[t1:t2+1], sst[t1:t2+1], clim['thresh'][t1:t2+1], \
-                     color=(1,0.6,0.5))
-# Find indices for MHW of interest (2011 WA event) and shade accordingly
-t1 = np.where(t==mhws['time_start'][ev])[0][0]
-t2 = np.where(t==mhws['time_end'][ev])[0][0]
-plt.fill_between(dates[t1:t2+1], sst[t1:t2+1], clim['thresh'][t1:t2+1], \
-                 color='r')
-# Plot SST, seasonal cycle, threshold, shade MHWs with main event in red
-plt.plot(dates, sst, 'k-', linewidth=2)
-plt.plot(dates, clim['thresh'], 'g-', linewidth=2)
-plt.plot(dates, clim['seas'], 'b-', linewidth=2)
-plt.title('SST (black), seasonal climatology (blue), \
-          threshold (green), detected MHW events (shading)')
-plt.xlim(mhws['time_start'][ev]-150, mhws['time_end'][ev]+150)
-plt.ylim(clim['seas'].min() - 1, clim['seas'].max() + mhws['intensity_max'][ev] + 0.5)
-plt.ylabel(r'SST [$^\circ$C]')
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<matplotlib.text.Text at 0x3999f10>
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Yep, It's certainly picked out the largest event in the series (dark red shading). This event also seems to have been preceded and succeeded by a number of shorter, weaker events (light red shading). Let's have a look at how the MHW statistics are distributed across all the detected events:

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plt.figure(figsize=(15,7))
-# Duration
-plt.subplot(2,2,1)
-evMax = np.argmax(mhws['duration'])
-plt.bar(range(mhws['n_events']), mhws['duration'], width=0.6, \
-        color=(0.7,0.7,0.7))
-plt.bar(evMax, mhws['duration'][evMax], width=0.6, color=(1,0.5,0.5))
-plt.bar(ev, mhws['duration'][ev], width=0.6, edgecolor=(1,0.,0.), \
-        color='none')
-plt.xlim(0, mhws['n_events'])
-plt.ylabel('[days]')
-plt.title('Duration')
-# Maximum intensity
-plt.subplot(2,2,2)
-evMax = np.argmax(mhws['intensity_max'])
-plt.bar(range(mhws['n_events']), mhws['intensity_max'], width=0.6, \
-        color=(0.7,0.7,0.7))
-plt.bar(evMax, mhws['intensity_max'][evMax], width=0.6, color=(1,0.5,0.5))
-plt.bar(ev, mhws['intensity_max'][ev], width=0.6, edgecolor=(1,0.,0.), \
-        color='none')
-plt.xlim(0, mhws['n_events'])
-plt.ylabel(r'[$^\circ$C]')
-plt.title('Maximum Intensity')
-# Mean intensity
-plt.subplot(2,2,4)
-evMax = np.argmax(mhws['intensity_mean'])
-plt.bar(range(mhws['n_events']), mhws['intensity_mean'], width=0.6, \
-        color=(0.7,0.7,0.7))
-plt.bar(evMax, mhws['intensity_mean'][evMax], width=0.6, color=(1,0.5,0.5))
-plt.bar(ev, mhws['intensity_mean'][ev], width=0.6, edgecolor=(1,0.,0.), \
-        color='none')
-plt.xlim(0, mhws['n_events'])
-plt.title('Mean Intensity')
-plt.ylabel(r'[$^\circ$C]')
-plt.xlabel('MHW event number')
-# Cumulative intensity
-plt.subplot(2,2,3)
-evMax = np.argmax(mhws['intensity_cumulative'])
-plt.bar(range(mhws['n_events']), mhws['intensity_cumulative'], width=0.6, \
-        color=(0.7,0.7,0.7))
-plt.bar(evMax, mhws['intensity_cumulative'][evMax], width=0.6, color=(1,0.5,0.5))
-plt.bar(ev, mhws['intensity_cumulative'][ev], width=0.6, edgecolor=(1,0.,0.), \
-        color='none')
-plt.xlim(0, mhws['n_events'])
-plt.title(r'Cumulative Intensity')
-plt.ylabel(r'[$^\circ$C$\times$days]')
-plt.xlabel('MHW event number')
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The largest event on record by duration, maximum intensity, mean intensity, and cumulative intensity (shown by red shaded bars) happens to be the 2011 event (red outlined bars).

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Case study #2: 2012 Northwest Atlantic event

We can also have a look at the 2012 Northwest Atlantic (NWA) event. Let's load a daily time series of SST from the NWA (67$^\circ$W, 43$^\circ$N) from the same data set as above and repeat the analysis:

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# Load Northwest Atlantic SST time series
-sst = np.loadtxt('data/sst_NW_Atl.csv', delimiter=',')
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-# Detect MHW events
-mhws, clim = mhw.detect(t, sst)
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-ev = np.argmax(mhws['intensity_max'])
-print 'Maximum intensity:', mhws['intensity_max'][ev], 'deg. C'
-print 'Average intensity:', mhws['intensity_mean'][ev], 'deg. C'
-print 'Cumulative intensity:', mhws['intensity_cumulative'][ev], 'deg. C-days'
-print 'Duration:', mhws['duration'][ev], 'days'
-print 'Start date:', mhws['date_start'][ev].strftime("%d %B %Y")
-print 'End date:', mhws['date_end'][ev].strftime("%d %B %Y")
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Maximum intensity: 4.91866851176 deg. C
-Average intensity: 2.61698414413 deg. C
-Cumulative intensity: 146.551112071 deg. C-days
-Duration: 56 days
-Start date: 10 April 2012
-End date: 04 June 2012
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Again, the event with largest maximum intensity turns out to be an event known in the literature: the 2012 NWA event. Let's plot it as above:

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In [11]:
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plt.figure(figsize=(14,10))
-plt.subplot(2,1,1)
-# Plot SST, seasonal cycle, and threshold
-plt.plot(dates, sst, 'k-')
-plt.plot(dates, clim['thresh'], 'g-')
-plt.plot(dates, clim['seas'], 'b-')
-plt.title('SST (black), seasonal climatology (blue), threshold (green), \
-           detected MHW events (shading)')
-plt.xlim(t[0], t[-1])
-plt.ylim(sst.min()-0.5, sst.max()+0.5)
-plt.ylabel(r'SST [$^\circ$C]')
-plt.subplot(2,1,2)
-# Find indices for all ten MHWs before and after event of interest and shade accordingly
-for ev0 in np.arange(ev-10, ev+11, 1):
-    t1 = np.where(t==mhws['time_start'][ev0])[0][0]
-    t2 = np.where(t==mhws['time_end'][ev0])[0][0]
-    plt.fill_between(dates[t1:t2+1], sst[t1:t2+1], clim['thresh'][t1:t2+1], \
-                     color=(1,0.6,0.5))
-# Find indices for MHW of interest (2012 NWA event) and shade accordingly
-t1 = np.where(t==mhws['time_start'][ev])[0][0]
-t2 = np.where(t==mhws['time_end'][ev])[0][0]
-plt.fill_between(dates[t1:t2+1], sst[t1:t2+1], clim['thresh'][t1:t2+1], color='r')
-# Plot SST, seasonal cycle, threshold, shade MHWs with main event in red
-plt.plot(dates, sst, 'k-', linewidth=2)
-plt.plot(dates, clim['thresh'], 'g-', linewidth=2)
-plt.plot(dates, clim['seas'], 'b-', linewidth=2)
-plt.title('SST (black), seasonal climatology (blue), threshold (green), \
-        detected MHW events (shading)')
-plt.xlim(mhws['time_start'][ev]-150, mhws['time_end'][ev]+150)
-plt.ylim(clim['seas'].min() - 1, clim['seas'].max() + \
-         mhws['intensity_max'][ev] + 0.5)
-plt.ylabel(r'SST [$^\circ$C]')
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<matplotlib.text.Text at 0x525fa90>
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Interestingly, the 2012 NWA event doesn't appear to be as intense as the 2011 WA event. That is partly because it occured outside the summer months. It is nonetheless the largest event on record according to maximum intensity:

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In [12]:
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plt.figure(figsize=(15,7))
-# Duration
-plt.subplot(2,2,1)
-evMax = np.argmax(mhws['duration'])
-plt.bar(range(mhws['n_events']), mhws['duration'], width=0.6, \
-        color=(0.7,0.7,0.7))
-plt.bar(evMax, mhws['duration'][evMax], width=0.6, color=(1,0.5,0.5))
-plt.bar(ev, mhws['duration'][ev], width=0.6, edgecolor=(1,0.,0.), \
-        color='none')
-plt.xlim(0, mhws['n_events'])
-plt.ylabel('[days]')
-plt.title('Duration')
-# Maximum intensity
-plt.subplot(2,2,2)
-evMax = np.argmax(mhws['intensity_max'])
-plt.bar(range(mhws['n_events']), mhws['intensity_max'], width=0.6, \
-        color=(0.7,0.7,0.7))
-plt.bar(evMax, mhws['intensity_max'][evMax], width=0.6, color=(1,0.5,0.5))
-plt.bar(ev, mhws['intensity_max'][ev], width=0.6, edgecolor=(1,0.,0.), \
-        color='none')
-plt.xlim(0, mhws['n_events'])
-plt.ylabel(r'[$^\circ$C]')
-plt.title('Maximum Intensity')
-# Mean intensity
-plt.subplot(2,2,4)
-evMax = np.argmax(mhws['intensity_mean'])
-plt.bar(range(mhws['n_events']), mhws['intensity_mean'], width=0.6, \
-        color=(0.7,0.7,0.7))
-plt.bar(evMax, mhws['intensity_mean'][evMax], width=0.6, color=(1,0.5,0.5))
-plt.bar(ev, mhws['intensity_mean'][ev], width=0.6, edgecolor=(1,0.,0.), \
-        color='none')
-plt.xlim(0, mhws['n_events'])
-plt.title('Mean Intensity')
-plt.ylabel(r'[$^\circ$C]')
-plt.xlabel('MHW event number')
-# Cumulative intensity
-plt.subplot(2,2,3)
-evMax = np.argmax(mhws['intensity_cumulative'])
-plt.bar(range(mhws['n_events']), mhws['intensity_cumulative'], width=0.6, \
-        color=(0.7,0.7,0.7))
-plt.bar(evMax, mhws['intensity_cumulative'][evMax], width=0.6, color=(1,0.5,0.5))
-plt.bar(ev, mhws['intensity_cumulative'][ev], width=0.6, edgecolor=(1,0.,0.), \
-        color='none')
-plt.xlim(0, mhws['n_events'])
-plt.title(r'Cumulative Intensity')
-plt.ylabel(r'[$^\circ$C$\times$days]')
-plt.xlabel('MHW event number')
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<matplotlib.text.Text at 0x65fb350>
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However, the 2012 NWA event (red outlined bars) is not the highest ranked event (red shaded bars) when sorted according to mean intensity, cumulative intenstiy and duration:

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In [13]:
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ranks = mhws['n_events']- np.array(mhws['duration']).argsort().argsort()
-print "The 2012 NWA event is ranked number " \
-        + str(ranks[ev]) + " by duration"
-ranks = mhws['n_events']- np.array(mhws['intensity_max']).argsort().argsort()
-print "The 2012 NWA event is ranked number " \
-        + str(ranks[ev]) + " by maximum intensity"
-ranks = mhws['n_events']- np.array(mhws['intensity_mean']).argsort().argsort()
-print "The 2012 NWA event is ranked number " \
-        + str(ranks[ev]) + " by mean intensity"
-ranks = mhws['n_events']- np.array(mhws['intensity_cumulative']).argsort().argsort()
-print "The 2012 NWA event is ranked number " \
-        + str(ranks[ev]) + " by cumulative intensity"
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The 2012 NWA event is ranked number 4 by duration
-The 2012 NWA event is ranked number 1 by maximum intensity
-The 2012 NWA event is ranked number 5 by mean intensity
-The 2012 NWA event is ranked number 4 by cumulative intensity
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Case study #3: 2003 Mediterranean event

We can also have a look at the 2003 Mediterranean (Med) event. Let's load a daily time series of SST from the Med just south of France (9$^\circ$E, 43.5$^\circ$N) from the same data set as above and repeat the analysis:

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In [14]:
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# Load Mediterranean SST time series
-sst = np.loadtxt('data/sst_Med.csv', delimiter=',')
-
-# Detect MHW events
-mhws, clim = mhw.detect(t, sst)
-
-# Find largest event
-ev = np.argmax(mhws['intensity_max'])
-print 'Maximum intensity:', mhws['intensity_max'][ev], 'deg. C'
-print 'Average intensity:', mhws['intensity_mean'][ev], 'deg. C'
-print 'Cumulative intensity:', mhws['intensity_cumulative'][ev], 'deg. C-days'
-print 'Duration:', mhws['duration'][ev], 'days'
-print 'Start date:', mhws['date_start'][ev].strftime("%d %B %Y")
-print 'End date:', mhws['date_end'][ev].strftime("%d %B %Y")
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Maximum intensity: 5.05790311275 deg. C
-Average intensity: 3.8816147715 deg. C
-Cumulative intensity: 34.9345329435 deg. C-days
-Duration: 9 days
-Start date: 26 June 2008
-End date: 04 July 2008
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We are looking for the 2003 Med event but the largest event on record, according to maximum intensity, occurred in 2008. However, the 2003 Med event is the largest according to mean intensity:

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In [15]:
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# Find largest event (by mean intensity)
-ev = np.argmax(mhws['intensity_mean'])
-print 'Maximum intensity:', mhws['intensity_max'][ev], 'deg. C'
-print 'Average intensity:', mhws['intensity_mean'][ev], 'deg. C'
-print 'Cumulative intensity:', mhws['intensity_cumulative'][ev], 'deg. C-days'
-print 'Duration:', mhws['duration'][ev], 'days'
-print 'Start date:', mhws['date_start'][ev].strftime("%d %B %Y")
-print 'End date:', mhws['date_end'][ev].strftime("%d %B %Y")
-
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Maximum intensity: 5.02474964331 deg. C
-Average intensity: 4.05484839422 deg. C
-Cumulative intensity: 121.645451826 deg. C-days
-Duration: 30 days
-Start date: 02 June 2003
-End date: 01 July 2003
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And a time series plot shows it clearly to be a large event:

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In [16]:
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plt.figure(figsize=(14,10))
-plt.subplot(2,1,1)
-# Plot SST, seasonal cycle, and threshold
-plt.plot(dates, sst, 'k-')
-plt.plot(dates, clim['thresh'], 'g-')
-plt.plot(dates, clim['seas'], 'b-')
-plt.title('SST (black), seasonal climatology (blue), threshold (green), \
-        detected MHW events (shading)')
-plt.xlim(t[0], t[-1])
-plt.ylim(sst.min()-0.5, sst.max()+0.5)
-plt.ylabel(r'SST [$^\circ$C]')
-plt.subplot(2,1,2)
-# Find indices for all ten MHWs before and after event of interest and shade accordingly
-for ev0 in np.arange(ev-10, ev+11, 1):
-    t1 = np.where(t==mhws['time_start'][ev0])[0][0]
-    t2 = np.where(t==mhws['time_end'][ev0])[0][0]
-    plt.fill_between(dates[t1:t2+1], sst[t1:t2+1], clim['thresh'][t1:t2+1], \
-                     color=(1,0.6,0.5))
-# Find indices for MHW of interest (2003 Med event) and shade accordingly
-t1 = np.where(t==mhws['time_start'][ev])[0][0]
-t2 = np.where(t==mhws['time_end'][ev])[0][0]
-plt.fill_between(dates[t1:t2+1], sst[t1:t2+1], clim['thresh'][t1:t2+1], color='r')
-# Plot SST, seasonal cycle, threshold, shade MHWs with main event in red
-plt.plot(dates, sst, 'k-', linewidth=2)
-plt.plot(dates, clim['thresh'], 'g-', linewidth=2)
-plt.plot(dates, clim['seas'], 'b-', linewidth=2)
-plt.title('SST (black), seasonal climatology (blue), threshold (green), \
-        detected MHW events (shading)')
-plt.xlim(mhws['time_start'][ev]-150, mhws['time_end'][ev]+150)
-plt.ylim(clim['seas'].min() - 1, clim['seas'].max()\
-         + mhws['intensity_max'][ev] + 0.5)
-plt.ylabel(r'SST [$^\circ$C]')
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<matplotlib.text.Text at 0x6eecfd0>
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And we can see where this event (red outlined bars) fits amongst all other detected events:

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In [17]:
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plt.figure(figsize=(15,7))
-# Duration
-plt.subplot(2,2,1)
-evMax = np.argmax(mhws['duration'])
-plt.bar(range(mhws['n_events']), mhws['duration'], width=0.6, \
-        color=(0.7,0.7,0.7))
-plt.bar(evMax, mhws['duration'][evMax], width=0.6, color=(1,0.5,0.5))
-plt.bar(ev, mhws['duration'][ev], width=0.6, edgecolor=(1,0.,0.), \
-        color='none')
-plt.xlim(0, mhws['n_events'])
-plt.ylabel('[days]')
-plt.title('Duration')
-# Maximum intensity
-plt.subplot(2,2,2)
-evMax = np.argmax(mhws['intensity_max'])
-plt.bar(range(mhws['n_events']), mhws['intensity_max'], width=0.6, \
-        color=(0.7,0.7,0.7))
-plt.bar(evMax, mhws['intensity_max'][evMax], width=0.6, color=(1,0.5,0.5))
-plt.bar(ev, mhws['intensity_max'][ev], width=0.6, edgecolor=(1,0.,0.), \
-        color='none')
-plt.xlim(0, mhws['n_events'])
-plt.ylabel(r'[$^\circ$C]')
-plt.title('Maximum Intensity')
-# Mean intensity
-plt.subplot(2,2,4)
-evMax = np.argmax(mhws['intensity_mean'])
-plt.bar(range(mhws['n_events']), mhws['intensity_mean'], width=0.6, \
-        color=(0.7,0.7,0.7))
-plt.bar(evMax, mhws['intensity_mean'][evMax], width=0.6, color=(1,0.5,0.5))
-plt.bar(ev, mhws['intensity_mean'][ev], width=0.6, edgecolor=(1,0.,0.), \
-        color='none')
-plt.xlim(0, mhws['n_events'])
-plt.title('Mean Intensity')
-plt.ylabel(r'[$^\circ$C]')
-plt.xlabel('MHW event number')
-# Cumulative intensity
-plt.subplot(2,2,3)
-evMax = np.argmax(mhws['intensity_cumulative'])
-plt.bar(range(mhws['n_events']), mhws['intensity_cumulative'], width=0.6, \
-        color=(0.7,0.7,0.7))
-plt.bar(evMax, mhws['intensity_cumulative'][evMax], width=0.6, color=(1,0.5,0.5))
-plt.bar(ev, mhws['intensity_cumulative'][ev], width=0.6, edgecolor=(1,0.,0.), \
-        color='none')
-plt.xlim(0, mhws['n_events'])
-plt.title(r'Cumulative Intensity')
-plt.ylabel(r'[$^\circ$C$\times$days]')
-plt.xlabel('MHW event number')
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ranks = mhws['n_events']- np.array(mhws['duration']).argsort().argsort()
-print "The 2003 Med event is ranked number " \
-        + str(ranks[ev]) + " by duration"
-ranks = mhws['n_events']- np.array(mhws['intensity_max']).argsort().argsort()
-print "The 2003 Med event is ranked number " \
-        + str(ranks[ev]) + " by maximum intensity"
-ranks = mhws['n_events']- np.array(mhws['intensity_mean']).argsort().argsort()
-print "The 2003 Med event is ranked number " \
-        + str(ranks[ev]) + " by mean intensity"
-ranks = mhws['n_events']- np.array(mhws['intensity_cumulative']).argsort().argsort()
-print "The 2003 Med event is ranked number " \
-        + str(ranks[ev]) + " by cumulative intensity"
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The 2003 Med event is ranked number 5 by duration
-The 2003 Med event is ranked number 2 by maximum intensity
-The 2003 Med event is ranked number 1 by mean intensity
-The 2003 Med event is ranked number 2 by cumulative intensity
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Block-averaged Marine Heatwave properties

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The marineHeatWaves (mhw) module also consists of functions to calculate the average of MHW properties over blocks in time (e.g., annually, decadally). The block-averaging function (blockAverage) takes as input a set of detected MHWs (i.e., the output from detect, the detection function described above) and outputs the MHW properties averaged over the specified block-length. This output can then be passed through the meanTrend function in order to calculate the time-mean and linear trend of the MHW properties over the measurement period.

-

Let's start by applying the block-averaging function to the Mediterranean MHWs which are stored in the variable mhws, using the default block length of 1 year (i.e., annual averages):

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mhwBlock = mhw.blockAverage(t, mhws)
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The variable mhwBlock has a set of keys which are time series of the MHW properties over the blocks. The central year of the blocks are stored in the key years_centre so we can look at, as an example, time series of MHW counts in each year and the average maximum intensity in each year:

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In [20]:
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plt.figure(figsize=(14,4))
-plt.subplot(1,2,1)
-plt.plot(mhwBlock['years_centre'], mhwBlock['count'], 'k-o')
-plt.ylim(0,9)
-plt.ylabel('[count]')
-plt.title('Number of MHWs by year')
-plt.subplot(1,2,2)
-plt.plot(mhwBlock['years_centre'], mhwBlock['intensity_max'], 'k-o')
-plt.ylabel(r'[$^\circ$C]')
-plt.title('Average MHW maximum intensity by year')
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<matplotlib.text.Text at 0x7f21bd0>
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There certainly looks like a positive trend in the annual number of MHWs and possibly in the maximum intensity as well. We can calculate the mean and trend of the MHW properties using the meanTrend function:

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In [22]:
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mean, trend = mhw.meanTrend(mhwBlock)
-print "There are on average " + str(mean['count']) + " MHWs in each year, \n \
-with a linear trend of " + str(10*trend['count']) + " MHW events per decade\n"
-print "The average maximum intensity is " + str(mean['intensity_max']) + " deg. C, \n \
-with a linear trend of " + str(10*trend['intensity_max']) + " deg. C per decade"
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There are on average 2.33333333333 MHWs in each year, 
- with a linear trend of 1.19986631016 MHW events per decade
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- with a linear trend of 0.18803154459 deg. C per decade
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Appendix: Function documentation

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detect

def detect(t, sst, climatologyPeriod=[1983,2012], pctile=90, windowHalfWidth=5, smoothPercentile=True, smoothPercentileWidth=31, minDuration=5, joinAcrossGaps=True, maxGap=2):

- -
Applies the Hobday et al. (2015) marine heat wave definition to an input time
-series of sst ('sst') along with a time vector ('t'). Outputs properties of
-all detected marine heat waves.
-
-Inputs:
-
-  t       Time vector, in datetime format (e.g., date(1982,1,1).toordinal())
-          [1D numpy array of length T]
-  sst     Temperature vector [1D numpy array of length T]
-
-Outputs:
-
-  mhw     Detected marine heat waves (MHWs). Each key (following list) is a
-          list of length N where N is the number of detected MHWs:
-
-    'time_start'           Start time of MHW [datetime format]
-    'time_end'             End time of MHW [datetime format]
-    'time_peak'            Time of MHW peak [datetime format]
-    'date_start'           Start date of MHW [datetime format]
-    'date_end'             End date of MHW [datetime format]
-    'date_peak'            Date of MHW peak [datetime format]
-    'duration'             Duration of MHW [days]
-    'intensity_max'        Maximum (peak) intensity [deg. C]
-    'intensity_mean'       Mean intensity [deg. C]
-    'intensity_var'        Intensity variability [deg. C]
-    'intensity_cumulative' Cumulative intensity [deg. C x days]
-    'rate_onset'           Onset rate of MHW [deg. C / days]
-    'rate_decline'         Decline rate of MHW [deg. C / days]
-
-    'intensity_max_relThresh', 'intensity_mean_relThresh', 'intensity_var_relThresh', 
-    and 'intensity_cumulative_relThresh' are as above except relative to the
-    threshold (e.g., 90th percentile) rather than the seasonal climatology
-
-    'n_events'             A scalar integer (not a list) indicating the total
-                           number of detected MHW events
-
-  clim    Climatology of SST. Each key (following list) is a seasonally-varying
-          time series [1D numpy array of length T] of a particular measure:
-
-    'thresh'               Seasonally varying threshold (e.g., 90th percentile)
-    'seas'                 Climatological seasonal cycle
-
-Options:
-
-  climatologyPeriod      Period over which climatology is calculated, specified
-                         as list of start and end years (DEFAULT = [1983,2012])
-  pctile                 Threshold percentile (%) for detection of extreme values
-                         (DEFAULT = 90)
-  windowHalfWidth        Width of window (one sided) about day-of-year used for
-                         the pooling of values and calculation of threshold percentile
-                         (DEFAULT = 5 [days])
-  smoothPercentile       Boolean switch indicating whether to smooth the threshold
-                         percentile timeseries with a moving average (DEFAULT = True)
-  smoothPercentileWidth  Width of moving average window for smoothing threshold
-                         (DEFAULT = 31 [days])
-  minDuration            Minimum duration for acceptance detected MHWs
-                         (DEFAULT = 5 [days])
-  joinAcrossGaps         Boolean switch indicating whether to join MHWs
-                         which occur before/after a short gap (DEFAULT = True)
-  maxGap                 Maximum length of gap allowed for the joining of MHWs
-                         (DEFAULT = 2 [days])
-
-Notes:
-
-  1. This function assumes that the input time series consist of continuous daily values
-     with no missing values.
-
-  2. This function supports leap years. This is done by ignoring Feb 29s for the initial
-     calculation of the climatology and threshold. The value of these for Feb 29 is then
-     linearly interpolated from the values for Feb 28 and Mar 1.
-
-  3. The calculation of onset and decline rates assumes that the heat wave started a half-day
-     before the start day and ended a half-day after the end-day. (This is consistent with the
-     duration definition as implemented, which assumes duration = end day - start day + 1.)
-
-Written by Eric Oliver, Institue for Marine and Antarctic Studies, University of Tasmania, Feb 2015
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blockAverage

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def blockAverage(t, mhw, blockLength=1):

- -
Calculate statistics of marine heatwave (MHW) properties averaged over blocks of
-a specified length of time. Takes as input a collection of detected MHWs
-(using the marineHeatWaves.detect function) and a time vector for the source
-SST series.
-
-Inputs:
-
-  t       Time vector, in datetime format (e.g., date(1982,1,1).toordinal())
-  mhw     Marine heat waves (MHWs) detected using marineHeatWaves.detect
-
-Outputs:
-
-  mhwBlock   Time series of block-averaged MHW properties. Each key (following list)
-             is a list of length N where N is the number of blocks:
-
-    'years_start'          Start year blocks (inclusive)
-    'years_end'            End year of blocks (inclusive)
-    'years_centre'         Decimal year at centre of blocks
-    'count'                Total MHW count in each block
-    'duration'             Average MHW duration in each block [days]
-    'intensity_max'        Average MHW "maximum (peak) intensity" in each block [deg. C]
-    'intensity_mean'       Average MHW "mean intensity" in each block [deg. C]
-    'intensity_var'        Average MHW "intensity variability" in each block [deg. C]
-    'intensity_cumulative' Average MHW "cumulative intensity" in each block [deg. C x days]
-    'rate_onset'           Average MHW onset rate in each block [deg. C / days]
-    'rate_decline'         Average MHW decline rate in each block [deg. C / days]
-
-    'intensity_max_relThresh', 'intensity_mean_relThresh', 'intensity_var_relThresh', 
-    and 'intensity_cumulative_relThresh' are as above except relative to the
-    threshold (e.g., 90th percentile) rather than the seasonal climatology
-
-Options:
-
-  blockLength            Size of block (in years) over which to calculate the
-                         averaged MHW properties. Must be an integer greater than
-                         or equal to 1 (DEFAULT = 1 [year])
-
-Notes:
-
-  This function assumes that the input time vector consists of continuous daily values.
-
-Written by Eric Oliver, Institue for Marine and Antarctic Studies, University of Tasmania, Feb-Mar 2015
- -
-
-
-
-
-
-
-
-

meanTrend

-
-
-
-
-
-
-
-
-

def meanTrend(mhwBlock):

- -
Calculates the mean and trend of marine heatwave (MHW) properties. Takes as input a
-collection of block-averaged MHW properties (using the marineHeatWaves.blockAverage
-function). Handles missing values (which should be specified by NaNs).
-
-Inputs:
-
-  mhwBlock      Time series of block-averaged MHW statistics calculated using the
-                marineHeatWaves.blockAverage function
-
-Outputs:
-
-  mean          Mean of all MHW properties over all block-averaged values
-  trend         Linear trend of all MHW properties over all block-averaged values
-
-                Both mean and trend have the following keys, the units the trend
-                are the units of the property of interest per year:
-
-    'duration'             Duration of MHW [days]
-    'intensity_max'        Maximum (peak) intensity [deg. C]
-    'intensity_mean'       Mean intensity [deg. C]
-    'intensity_var'        Intensity variability [deg. C]
-    'intensity_cumulative' Cumulative intensity [deg. C x days]
-    'rate_onset'           Onset rate of MHW [deg. C / days]
-    'rate_decline'         Decline rate of MHW [deg. C / days]
-
-    'intensity_max_relThresh', 'intensity_mean_relThresh', 'intensity_var_relThresh', 
-    and 'intensity_cumulative_relThresh' are as above except relative to the
-    threshold (e.g., 90th percentile) rather than the seasonal climatology
-
-Notes:
-
-  This calculation performs a multiple linear regression of the form
-    y ~ beta * X + eps
-  where y is the MHW property of interest and X is a matrix of predictors. The first
-  column of X is all ones to estimate the mean, the second column is the time vector
-  which is taken as mhwBlock['years_centre'] and offset to be equal to zero at its
-  mid-point.
-
-Written by Eric Oliver, Institue for Marine and Antarctic Studies, University of Tasmania, Feb-Mar 2015
- -
-
-
-
-
-
In [ ]:
-
-
-
 
-
- -
-
-
- -
-
-
- - diff --git a/docs/example_synthetic.html b/docs/example_synthetic.html index 5792648..8a2c5a2 100644 --- a/docs/example_synthetic.html +++ b/docs/example_synthetic.html @@ -186,7 +186,7 @@

Marine Heatwaves Definition
-

This document describes the marineHeatWaves module for python which implements the Marine Heatwave (MHW) definition of Hobday et al. (manuscript in preparation). This software is demonstrated by applying the MHW definition to a stochastic red noise process. This was developed as an interactive ipython notebook which the user can run themselves provided they have the required python modules (numpy, scipy, datetime, and matplotlib).

+

This document describes the marineHeatWaves module for python which implements the Marine Heatwave (MHW) definition of Hobday et al. (manuscript submitted to Progress in Oceanography). This software is demonstrated by applying the MHW definition to a stochastic red noise process. This was developed as an interactive ipython notebook which the user can run themselves provided they have the required python modules (numpy, scipy, datetime, and matplotlib).

@@ -257,7 +257,7 @@

Generate synthetic temperatu
-
In [3]:
+
In [10]:
# Generate time vector using datetime format (January 1 of year 1 is day 1)
@@ -268,7 +268,7 @@ 

Generate synthetic temperatu sst[0] = 0 # Initial condition a = 0.85 # autoregressive parameter for i in range(1,len(t)): - sst[i] = a*sst[i-1] + 0.85*np.random.randn() + 0.5*np.cos(t[i]*2*np.pi/365.25) + sst[i] = a*sst[i-1] + 0.75*np.random.randn() + 0.5*np.cos(t[i]*2*np.pi/365.25) sst = sst - sst.min() + 5.

@@ -289,7 +289,7 @@

Marine Heatwave Detection
-
In [4]:
+
In [11]:
mhws, clim = mhw.detect(t, sst)
@@ -312,7 +312,7 @@ 

Marine Heatwave Detection
-
In [5]:
+
In [12]:
mhws['n_events']
@@ -326,11 +326,11 @@ 

Marine Heatwave Detection -
Out[5]:
+
Out[12]:
-
68
+
65
@@ -351,7 +351,7 @@

Marine Heatwave Detection
-
In [6]:
+
In [13]:
mhws['intensity_max'][0:10]
@@ -365,20 +365,20 @@ 

Marine Heatwave Detection -
Out[6]:
+
Out[13]:
-
[2.3970125030807203,
- 3.4964158273610586,
- 4.647740471932174,
- 3.7980800279010012,
- 4.3660263915303794,
- 2.7839414498476138,
- 4.6494430410442433,
- 4.0000743829522953,
- 4.5810991764288893,
- 3.9387834314425056]
+
[3.3455745852780989,
+ 3.5165101781833101,
+ 3.5094426025360832,
+ 2.8836950818283675,
+ 4.5281645612607484,
+ 3.6626085409989937,
+ 3.1642501721248628,
+ 3.0971113963048715,
+ 3.5946579814024702,
+ 3.1679283319142293]
@@ -399,7 +399,7 @@

Marine Heatwave Detection
-
In [7]:
+
In [14]:
@@ -447,7 +447,7 @@

Marine Heatwave Detection
-
In [8]:
+
In [15]:
plt.figure(figsize=(14,10))
@@ -492,11 +492,11 @@ 

Marine Heatwave Detection - @@ -2827,7 +2748,7 @@

Marine Heatwave Detection
-
In [9]:
+
In [16]:
plt.figure(figsize=(15,7))
@@ -2887,11 +2808,11 @@ 

Marine Heatwave Detection -
Out[9]:
+
Out[16]:
-
<matplotlib.text.Text at 0x4615490>
+
<matplotlib.text.Text at 0x58708d0>
@@ -2900,380 +2821,351 @@

Marine Heatwave Detection -Marine Heatwave Detection + +

+
+
+
+
+
+

We can even look at the return periods for events with those properties:

+ +
+
+
+
+
+
In [20]:
+
+
+
print "The return period for an event with this duration was " \
+        + str(returnPeriod['duration'][ev]) + " years"
+print "The return period for an event with this maximum intensity was " \
+        + str(returnPeriod['intensity_max'][ev]) + " years"
+print "The return period for an event with this mean intensity was " \
+        + str(returnPeriod['intensity_mean'][ev]) + " years"
+print "The return period for an event with this cumulative intensity was " \
+        + str(returnPeriod['intensity_cumulative'][ev]) + " years"
+
+ +
+
+
+ +
+
+ + +
+
+
The return period for an event with this duration was 5.66655258955 years
+The return period for an event with this maximum intensity was 33.9993155373 years
+The return period for an event with this mean intensity was 4.85704507676 years
+The return period for an event with this cumulative intensity was 4.85704507676 years
 
@@ -3357,7 +3293,7 @@

Block-averaged Marine Heatwav

-
In [11]:
+
In [21]:
mhwBlock = mhw.blockAverage(t, mhws)
@@ -3380,7 +3316,7 @@ 

Block-averaged Marine Heatwav

-
In [12]:
+
In [22]:
plt.figure(figsize=(14,4))
@@ -3403,11 +3339,11 @@ 

Block-averaged Marine Heatwav
-
Out[12]:
+
Out[22]:
-
<matplotlib.text.Text at 0x4cbb290>
+
<matplotlib.text.Text at 0x6565810>
@@ -3417,451 +3353,473 @@

Block-averaged Marine Heatwav
@@ -3884,14 +3842,19 @@

Block-averaged Marine Heatwav

-
In [13]:
+
In [23]:
mean, trend, dtrend = mhw.meanTrend(mhwBlock)
 print "There are on average " + str(mean['count']) + " MHWs in each year, \n \
-with a linear trend of " + str(10*trend['count']) + " MHW events per decade\n"
+with a linear trend of " + str(10*trend['count']) + " MHW events per decade \n \
+This trend is statistically significant (p<0.05): " \
++ str(np.abs(trend['count']) > dtrend['count']) + "\n"
+
 print "The average maximum intensity is " + str(mean['intensity_max']) + " deg. C, \n \
-with a linear trend of " + str(10*trend['intensity_max']) + " deg. C per decade"
+with a linear trend of " + str(10*trend['intensity_max']) + " deg. C per decade \n \
+This trend is statistically significant (p<0.05): " \
++ str(np.abs(trend['intensity_max']) > dtrend['intensity_max'])
 
@@ -3904,11 +3867,13 @@

Block-averaged Marine Heatwav
-
There are on average 2.06060606061 MHWs in each year, 
- with a linear trend of 0.24064171123 MHW events per decade
+
There are on average 1.9696969697 MHWs in each year, 
+ with a linear trend of -0.116978609626 MHW events per decade 
+ This trend is statistically significant (p<0.05): False
 
-The average maximum intensity is 4.03496291446 deg. C, 
- with a linear trend of 0.0371253287557 deg. C per decade
+The average maximum intensity is 3.41722975039 deg. C, 
+ with a linear trend of -0.0677028401646 deg. C per decade 
+ This trend is statistically significant (p<0.05): False
 
diff --git a/docs/example_synthetic.ipynb b/docs/example_synthetic.ipynb index 8058b60..766c515 100644 --- a/docs/example_synthetic.ipynb +++ b/docs/example_synthetic.ipynb @@ -11,7 +11,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This document describes the `marineHeatWaves` module for python which implements the Marine Heatwave (MHW) definition of Hobday et al. (*manuscript in preparation*). This software is demonstrated by applying the MHW definition to a stochastic red noise process. This was developed as an interactive ipython notebook which the user can run themselves provided they have the required python modules (`numpy`, `scipy`, `datetime`, and `matplotlib`)." + "This document describes the `marineHeatWaves` module for python which implements the Marine Heatwave (MHW) definition of Hobday et al. (*manuscript submitted to Progress in Oceanography*). This software is demonstrated by applying the MHW definition to a stochastic red noise process. This was developed as an interactive ipython notebook which the user can run themselves provided they have the required python modules (`numpy`, `scipy`, `datetime`, and `matplotlib`)." ] }, { @@ -65,7 +65,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 10, "metadata": { "collapsed": false }, @@ -79,7 +79,7 @@ "sst[0] = 0 # Initial condition\n", "a = 0.85 # autoregressive parameter\n", "for i in range(1,len(t)):\n", - " sst[i] = a*sst[i-1] + 0.85*np.random.randn() + 0.5*np.cos(t[i]*2*np.pi/365.25)\n", + " sst[i] = a*sst[i-1] + 0.75*np.random.randn() + 0.5*np.cos(t[i]*2*np.pi/365.25)\n", "sst = sst - sst.min() + 5." ] }, @@ -94,7 +94,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 11, "metadata": { "collapsed": false }, @@ -112,7 +112,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 12, "metadata": { "collapsed": false }, @@ -120,10 +120,10 @@ { "data": { "text/plain": [ - "68" + "65" ] }, - "execution_count": 5, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } @@ -141,7 +141,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 13, "metadata": { "collapsed": false }, @@ -149,19 +149,19 @@ { "data": { "text/plain": [ - "[2.3970125030807203,\n", - " 3.4964158273610586,\n", - " 4.647740471932174,\n", - " 3.7980800279010012,\n", - " 4.3660263915303794,\n", - " 2.7839414498476138,\n", - " 4.6494430410442433,\n", - " 4.0000743829522953,\n", - " 4.5810991764288893,\n", - " 3.9387834314425056]" + "[3.3455745852780989,\n", + " 3.5165101781833101,\n", + " 3.5094426025360832,\n", + " 2.8836950818283675,\n", + " 4.5281645612607484,\n", + " 3.6626085409989937,\n", + " 3.1642501721248628,\n", + " 3.0971113963048715,\n", + " 3.5946579814024702,\n", + " 3.1679283319142293]" ] }, - "execution_count": 6, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } @@ -179,7 +179,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 14, "metadata": { "collapsed": false }, @@ -188,12 +188,12 @@ "name": "stdout", "output_type": "stream", "text": [ - "Maximum intensity: 5.84393386465 deg. C\n", - "Average intensity: 3.6080114723 deg. C\n", - "Cumulative intensity: 144.320458892 deg. C-days\n", - "Duration: 40 days\n", - "Start date: 31 July 2003\n", - "End date: 08 September 2003\n" + "Maximum intensity: 4.80172612888 deg. C\n", + "Average intensity: 2.9970910959 deg. C\n", + "Cumulative intensity: 47.9534575345 deg. C-days\n", + "Duration: 16 days\n", + "Start date: 22 November 1989\n", + "End date: 07 December 1989\n" ] } ], @@ -216,7 +216,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 15, "metadata": { "collapsed": false }, @@ -224,2319 +224,2240 @@ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 8, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ - "iVBORw0KGgoAAAANSUhEUgAAA0sAAAJZCAYAAAB4La5SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", - "AAALEgAACxIB0t1+/AAAIABJREFUeJzsnXmcnVWR97/VW9budDaydSBsgbAGhRBUdgEREVFBBReU\n", - "0UGdUUedGbcxtNs4+vqqo+PyOjPuO444Mi4sEgVBUAdBQHZCAtmX7uzppPu8f9R57nOe5z739r3P\n", - "c253buf8Pp/+9H2WW8+59dSpU3WqTh0xxhAQEBAQEBAQEBAQEBCQRMtoNyAgICAgICAgICAgIGB/\n", - "RHCWAgICAgICAgICAgICMhCcpYCAgICAgICAgICAgAwEZykgICAgICAgICAgICADwVkKCAgICAgI\n", - "CAgICAjIQHCWAgICAgICAgICAgICMhCcpYD9BiJygYj82DkeEpHDKtx7lYjc5uGZmc8QkXEi8hcR\n", - 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"execution_count": 10, + "execution_count": 17, "metadata": { "collapsed": false }, @@ -3056,26 +2948,59 @@ "name": "stdout", "output_type": "stream", "text": [ - "The 2012 NWA event is ranked number 1 by duration\n", + "The 2012 NWA event is ranked number 6 by duration\n", "The 2012 NWA event is ranked number 1 by maximum intensity\n", - "The 2012 NWA event is ranked number 8 by mean intensity\n", - "The 2012 NWA event is ranked number 1 by cumulative intensity\n" + "The 2012 NWA event is ranked number 7 by mean intensity\n", + "The 2012 NWA event is ranked number 7 by cumulative intensity\n" ] } ], "source": [ - "ranks = mhws['n_events']- np.array(mhws['duration']).argsort().argsort()\n", + "rank, returnPeriod = mhw.rank(t, mhws)\n", "print \"The 2012 NWA event is ranked number \" \\\n", - " + str(ranks[ev]) + \" by duration\"\n", - "ranks = mhws['n_events']- np.array(mhws['intensity_max']).argsort().argsort()\n", + " + str(rank['duration'][ev]) + \" by duration\"\n", "print \"The 2012 NWA event is ranked number \" \\\n", - " + str(ranks[ev]) + \" by maximum intensity\"\n", - "ranks = mhws['n_events']- np.array(mhws['intensity_mean']).argsort().argsort()\n", + " + str(rank['intensity_max'][ev]) + \" by maximum intensity\"\n", "print \"The 2012 NWA event is ranked number \" \\\n", - " + str(ranks[ev]) + \" by mean intensity\"\n", - "ranks = mhws['n_events']- np.array(mhws['intensity_cumulative']).argsort().argsort()\n", + " + str(rank['intensity_mean'][ev]) + \" by mean intensity\"\n", "print \"The 2012 NWA event is ranked number \" \\\n", - " + str(ranks[ev]) + \" by cumulative intensity\"" + " + str(rank['intensity_cumulative'][ev]) + \" by cumulative intensity\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can even look at the return periods for events with those properties:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The return period for an event with this duration was 5.66655258955 years\n", + "The return period for an event with this maximum intensity was 33.9993155373 years\n", + "The return period for an event with this mean intensity was 4.85704507676 years\n", + "The return period for an event with this cumulative intensity was 4.85704507676 years\n" + ] + } + ], + "source": [ + "print \"The return period for an event with this duration was \" \\\n", + " + str(returnPeriod['duration'][ev]) + \" years\"\n", + "print \"The return period for an event with this maximum intensity was \" \\\n", + " + str(returnPeriod['intensity_max'][ev]) + \" years\"\n", + "print \"The return period for an event with this mean intensity was \" \\\n", + " + str(returnPeriod['intensity_mean'][ev]) + \" years\"\n", + "print \"The return period for an event with this cumulative intensity was \" \\\n", + " + str(returnPeriod['intensity_cumulative'][ev]) + \" years\"" ] }, { @@ -3096,7 +3021,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 21, "metadata": { "collapsed": false }, @@ -3114,7 +3039,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 22, "metadata": { "collapsed": false }, @@ -3122,10 +3047,10 @@ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 12, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, @@ -3133,454 +3058,476 @@ "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAz8AAAEKCAYAAAA8fet0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", - "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XnYJFV5/vHvDcguIKswIAMDRkFBGEDcxx1wjVtcUYyK\n", - "mjiYqDGaX2TiEmOMUUeNEjdEjfu+obgMoKAy7IIIDiD7DgPKIsLz++OcZurt6aW6u6q7ut/7c11z\n", - "zdvV1VWnq7ur6jnLcxQRmJmZmZmZzbp1Jl0AMzMzMzOzcXDwY2ZmZmZm84KDHzMzMzMzmxcc/JiZ\n", - "mZmZ2bzg4MfMzMzMzOYFBz9mZmZmZjYvOPixiZN0tKR3THD/n5Z0g6RfTqoMo5J0t6RdJ10OMzOr\n", - "n6T7SbpFkiZdlnaSvi/pJZMuR5Gkj0r6fxVta5mkz1axLZsMBz+2FkkXS7pa0saFZa+Q9LOadhn5\n", - 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"TeaG+O8wYDbhZtg7Y5k3T7zmr2LbrwYObcpxKaouLT4u64BHgCfje3LXFh+XGXUhZNep/Xus4LYZ\n", + "i/NUUXVpyGdP56mGnadiOcbiXFVUPZpwXIasyzp0nnrxnyY5FRERERGRiVBVwgMREREREZFaKfgR\n", + "EREREZGJoOBHREREREQmgoIfERERERGZCAp+RERERERkIij4ERERERGRiaDgR0REREREJoKCHxER\n", + "ERERmQj/D6B8M/apt7V1AAAAAElFTkSuQmCC\n" ], "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3609,7 +3556,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 23, "metadata": { "collapsed": false }, @@ -3618,20 +3565,27 @@ "name": "stdout", "output_type": "stream", "text": [ - "There are on average 2.06060606061 MHWs in each year, \n", - " with a linear trend of 0.24064171123 MHW events per decade\n", + "There are on average 1.9696969697 MHWs in each year, \n", + " with a linear trend of -0.116978609626 MHW events per decade \n", + " This trend is statistically significant (p<0.05): False\n", "\n", - "The average maximum intensity is 4.03496291446 deg. C, \n", - " with a linear trend of 0.0371253287557 deg. C per decade\n" + "The average maximum intensity is 3.41722975039 deg. C, \n", + " with a linear trend of -0.0677028401646 deg. C per decade \n", + " This trend is statistically significant (p<0.05): False\n" ] } ], "source": [ "mean, trend, dtrend = mhw.meanTrend(mhwBlock)\n", "print \"There are on average \" + str(mean['count']) + \" MHWs in each year, \\n \\\n", - "with a linear trend of \" + str(10*trend['count']) + \" MHW events per decade\\n\"\n", + "with a linear trend of \" + str(10*trend['count']) + \" MHW events per decade \\n \\\n", + "This trend is statistically significant (p<0.05): \" \\\n", + "+ str(np.abs(trend['count']) > dtrend['count']) + \"\\n\"\n", + "\n", "print \"The average maximum intensity is \" + str(mean['intensity_max']) + \" deg. C, \\n \\\n", - "with a linear trend of \" + str(10*trend['intensity_max']) + \" deg. C per decade\"" + "with a linear trend of \" + str(10*trend['intensity_max']) + \" deg. C per decade \\n \\\n", + "This trend is statistically significant (p<0.05): \" \\\n", + "+ str(np.abs(trend['intensity_max']) > dtrend['intensity_max'])" ] } ], diff --git a/docs/marineHeatWaves_manual.html b/docs/marineHeatWaves_manual.html new file mode 100644 index 0000000..a7df255 --- /dev/null +++ b/docs/marineHeatWaves_manual.html @@ -0,0 +1,9838 @@ + + + + + +marineHeatWaves_manual + + + + + + + + + + + + + + + + + + + + + + +
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+

Marine Heatwaves Definition

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This document describes the marineHeatWaves module for python which implements the Marine Heatwave (MHW) definition of Hobday et al. (manuscript submitted to Progress in Oceanography). This software is demonstrated by applying the MHW definition to observed SST records and showing how it identifies three historical MHWs: the 2011 Western Australia event, the 2012 Northwest Atlantic event, and the 2003 Mediterranean event. This was developed as an interactive ipython notebook which the user can run themselves provided they have the required python modules (numpy, scipy, datetime, and matplotlib).

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In [1]:
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# Load required modules
+import numpy as np
+from datetime import date
+from matplotlib import pyplot as plt
+%pylab inline
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+
Populating the interactive namespace from numpy and matplotlib
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In [2]:
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# Load marineHeatWaves definition module
+import marineHeatWaves as mhw
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In [3]:
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# Load WA SST time series
+sst = np.loadtxt('data/sst_WA.csv', delimiter=',')
+# Generate time vector using datetime format (January 1 of year 1 is day 1)
+t = np.arange(date(1982,1,1).toordinal(),date(2014,12,31).toordinal()+1)
+dates = [date.fromordinal(tt.astype(int)) for tt in t]
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Next we run the MHW detection algorithm which returns the variable mhws, consisting of the detected MHWs, and clim, consisting of the climatological (varying by day-of-year) seasonal cycle and extremes threshold:

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In [4]:
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mhws, clim = mhw.detect(t, sst)
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This algorithm has detected the following number of MHW events:

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In [5]:
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mhws['n_events']
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Out[5]:
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59
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The first ten events, for example, have the following maximum intensities (in $^\circ$C):

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In [6]:
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mhws['intensity_max'][0:10]
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Out[6]:
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[1.9217682854908773,
+ 2.1062844103988816,
+ 2.2164887090108891,
+ 1.8303919434472782,
+ 1.4887164867636926,
+ 1.4256402418392469,
+ 2.189464271687271,
+ 1.1276255857437931,
+ 1.9773352441706606,
+ 1.5506842273140933]
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Let's have a look at some properties of the event with the largest maximum intensity

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In [7]:
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ev = np.argmax(mhws['intensity_max']) # Find largest event
+print 'Maximum intensity:', mhws['intensity_max'][ev], 'deg. C'
+print 'Average intensity:', mhws['intensity_mean'][ev], 'deg. C'
+print 'Cumulative intensity:', mhws['intensity_cumulative'][ev], 'deg. C-days'
+print 'Duration:', mhws['duration'][ev], 'days'
+print 'Start date:', mhws['date_start'][ev].strftime("%d %B %Y")
+print 'End date:', mhws['date_end'][ev].strftime("%d %B %Y")
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Maximum intensity: 6.50649252319 deg. C
+Average intensity: 3.21216499826 deg. C
+Cumulative intensity: 192.729899895 deg. C-days
+Duration: 60 days
+Start date: 06 February 2011
+End date: 06 April 2011
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This turns out to be the infamous 2011 MHW off WA. Let's plot the SST time series over the full record and also have a closer look at the identified MHW event:

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In [8]:
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plt.figure(figsize=(14,10))
+plt.subplot(2,1,1)
+# Plot SST, seasonal cycle, and threshold
+plt.plot(dates, sst, 'k-')
+plt.plot(dates, clim['thresh'], 'g-')
+plt.plot(dates, clim['seas'], 'b-')
+plt.title('SST (black), seasonal climatology (blue), \
+          threshold (green), detected MHW events (shading)')
+plt.xlim(t[0], t[-1])
+plt.ylim(sst.min()-0.5, sst.max()+0.5)
+plt.ylabel(r'SST [$^\circ$C]')
+plt.subplot(2,1,2)
+# Find indices for all ten MHWs before and after event of interest and shade accordingly
+for ev0 in np.arange(ev-10, ev+11, 1):
+    t1 = np.where(t==mhws['time_start'][ev0])[0][0]
+    t2 = np.where(t==mhws['time_end'][ev0])[0][0]
+    plt.fill_between(dates[t1:t2+1], sst[t1:t2+1], clim['thresh'][t1:t2+1], \
+                     color=(1,0.6,0.5))
+# Find indices for MHW of interest (2011 WA event) and shade accordingly
+t1 = np.where(t==mhws['time_start'][ev])[0][0]
+t2 = np.where(t==mhws['time_end'][ev])[0][0]
+plt.fill_between(dates[t1:t2+1], sst[t1:t2+1], clim['thresh'][t1:t2+1], \
+                 color='r')
+# Plot SST, seasonal cycle, threshold, shade MHWs with main event in red
+plt.plot(dates, sst, 'k-', linewidth=2)
+plt.plot(dates, clim['thresh'], 'g-', linewidth=2)
+plt.plot(dates, clim['seas'], 'b-', linewidth=2)
+plt.title('SST (black), seasonal climatology (blue), \
+          threshold (green), detected MHW events (shading)')
+plt.xlim(mhws['time_start'][ev]-150, mhws['time_end'][ev]+150)
+plt.ylim(clim['seas'].min() - 1, clim['seas'].max() + mhws['intensity_max'][ev] + 0.5)
+plt.ylabel(r'SST [$^\circ$C]')
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Out[8]:
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<matplotlib.text.Text at 0x38cf610>
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Yep, It's certainly picked out the largest event in the series (dark red shading). This event also seems to have been preceded and succeeded by a number of shorter, weaker events (light red shading). Let's have a look at how the MHW statistics are distributed across all the detected events:

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In [9]:
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plt.figure(figsize=(15,7))
+# Duration
+plt.subplot(2,2,1)
+evMax = np.argmax(mhws['duration'])
+plt.bar(range(mhws['n_events']), mhws['duration'], width=0.6, \
+        color=(0.7,0.7,0.7))
+plt.bar(evMax, mhws['duration'][evMax], width=0.6, color=(1,0.5,0.5))
+plt.bar(ev, mhws['duration'][ev], width=0.6, edgecolor=(1,0.,0.), \
+        color='none')
+plt.xlim(0, mhws['n_events'])
+plt.ylabel('[days]')
+plt.title('Duration')
+# Maximum intensity
+plt.subplot(2,2,2)
+evMax = np.argmax(mhws['intensity_max'])
+plt.bar(range(mhws['n_events']), mhws['intensity_max'], width=0.6, \
+        color=(0.7,0.7,0.7))
+plt.bar(evMax, mhws['intensity_max'][evMax], width=0.6, color=(1,0.5,0.5))
+plt.bar(ev, mhws['intensity_max'][ev], width=0.6, edgecolor=(1,0.,0.), \
+        color='none')
+plt.xlim(0, mhws['n_events'])
+plt.ylabel(r'[$^\circ$C]')
+plt.title('Maximum Intensity')
+# Mean intensity
+plt.subplot(2,2,4)
+evMax = np.argmax(mhws['intensity_mean'])
+plt.bar(range(mhws['n_events']), mhws['intensity_mean'], width=0.6, \
+        color=(0.7,0.7,0.7))
+plt.bar(evMax, mhws['intensity_mean'][evMax], width=0.6, color=(1,0.5,0.5))
+plt.bar(ev, mhws['intensity_mean'][ev], width=0.6, edgecolor=(1,0.,0.), \
+        color='none')
+plt.xlim(0, mhws['n_events'])
+plt.title('Mean Intensity')
+plt.ylabel(r'[$^\circ$C]')
+plt.xlabel('MHW event number')
+# Cumulative intensity
+plt.subplot(2,2,3)
+evMax = np.argmax(mhws['intensity_cumulative'])
+plt.bar(range(mhws['n_events']), mhws['intensity_cumulative'], width=0.6, \
+        color=(0.7,0.7,0.7))
+plt.bar(evMax, mhws['intensity_cumulative'][evMax], width=0.6, color=(1,0.5,0.5))
+plt.bar(ev, mhws['intensity_cumulative'][ev], width=0.6, edgecolor=(1,0.,0.), \
+        color='none')
+plt.xlim(0, mhws['n_events'])
+plt.title(r'Cumulative Intensity')
+plt.ylabel(r'[$^\circ$C$\times$days]')
+plt.xlabel('MHW event number')
+
+ +
+
+
+ +
+
+ + +
Out[9]:
+ + +
+
<matplotlib.text.Text at 0x4aa07d0>
+
+ +
+ +
+ + +
+ +
+ +
+ +
+
+ +
+
+
+
+
+
+

The largest event on record by maximum intensity and mean intensity (shown by red shaded bars) and the second largest by duration and cumulative intensity happens to be the 2011 event (red outlined bars).

+ +
+
+
+
+
+
+
+
+

Case study #2: 2012 Northwest Atlantic event

We can also have a look at the 2012 Northwest Atlantic (NWA) event. Let's load a daily time series of SST from the NWA (67$^\circ$W, 43$^\circ$N) from the same data set as above and repeat the analysis:

+ +
+
+
+
+
+
In [10]:
+
+
+
# Load Northwest Atlantic SST time series
+sst = np.loadtxt('data/sst_NW_Atl.csv', delimiter=',')
+
+# Detect MHW events
+mhws, clim = mhw.detect(t, sst)
+
+# Find largest event
+ev = np.argmax(mhws['intensity_max'])
+print 'Maximum intensity:', mhws['intensity_max'][ev], 'deg. C'
+print 'Average intensity:', mhws['intensity_mean'][ev], 'deg. C'
+print 'Cumulative intensity:', mhws['intensity_cumulative'][ev], 'deg. C-days'
+print 'Duration:', mhws['duration'][ev], 'days'
+print 'Start date:', mhws['date_start'][ev].strftime("%d %B %Y")
+print 'End date:', mhws['date_end'][ev].strftime("%d %B %Y")
+
+ +
+
+
+ +
+
+ + +
+
+
Maximum intensity: 4.88888063364 deg. C
+Average intensity: 2.58685853386 deg. C
+Cumulative intensity: 144.864077896 deg. C-days
+Duration: 56 days
+Start date: 10 April 2012
+End date: 04 June 2012
+
+
+
+ +
+
+ +
+
+
+
+
+
+

Again, the event with largest maximum intensity turns out to be an event known in the literature: the 2012 NWA event. Let's plot it as above:

+ +
+
+
+
+
+
In [11]:
+
+
+
plt.figure(figsize=(14,10))
+plt.subplot(2,1,1)
+# Plot SST, seasonal cycle, and threshold
+plt.plot(dates, sst, 'k-')
+plt.plot(dates, clim['thresh'], 'g-')
+plt.plot(dates, clim['seas'], 'b-')
+plt.title('SST (black), seasonal climatology (blue), threshold (green), \
+           detected MHW events (shading)')
+plt.xlim(t[0], t[-1])
+plt.ylim(sst.min()-0.5, sst.max()+0.5)
+plt.ylabel(r'SST [$^\circ$C]')
+plt.subplot(2,1,2)
+# Find indices for all ten MHWs before and after event of interest and shade accordingly
+for ev0 in np.arange(ev-10, ev+11, 1):
+    t1 = np.where(t==mhws['time_start'][ev0])[0][0]
+    t2 = np.where(t==mhws['time_end'][ev0])[0][0]
+    plt.fill_between(dates[t1:t2+1], sst[t1:t2+1], clim['thresh'][t1:t2+1], \
+                     color=(1,0.6,0.5))
+# Find indices for MHW of interest (2012 NWA event) and shade accordingly
+t1 = np.where(t==mhws['time_start'][ev])[0][0]
+t2 = np.where(t==mhws['time_end'][ev])[0][0]
+plt.fill_between(dates[t1:t2+1], sst[t1:t2+1], clim['thresh'][t1:t2+1], color='r')
+# Plot SST, seasonal cycle, threshold, shade MHWs with main event in red
+plt.plot(dates, sst, 'k-', linewidth=2)
+plt.plot(dates, clim['thresh'], 'g-', linewidth=2)
+plt.plot(dates, clim['seas'], 'b-', linewidth=2)
+plt.title('SST (black), seasonal climatology (blue), threshold (green), \
+        detected MHW events (shading)')
+plt.xlim(mhws['time_start'][ev]-150, mhws['time_end'][ev]+150)
+plt.ylim(clim['seas'].min() - 1, clim['seas'].max() + \
+         mhws['intensity_max'][ev] + 0.5)
+plt.ylabel(r'SST [$^\circ$C]')
+
+ +
+
+
+ +
+
+ + +
Out[11]:
+ + +
+
<matplotlib.text.Text at 0x512ab10>
+
+ +
+ +
+ + +
+ +
+ +
+ +
+
+ +
+
+
+
+
+
+

Interestingly, the 2012 NWA event doesn't appear to be as intense as the 2011 WA event. That is partly because it occured outside the summer months. It is nonetheless the largest event on record according to maximum intensity:

+ +
+
+
+
+
+
In [12]:
+
+
+
plt.figure(figsize=(15,7))
+# Duration
+plt.subplot(2,2,1)
+evMax = np.argmax(mhws['duration'])
+plt.bar(range(mhws['n_events']), mhws['duration'], width=0.6, \
+        color=(0.7,0.7,0.7))
+plt.bar(evMax, mhws['duration'][evMax], width=0.6, color=(1,0.5,0.5))
+plt.bar(ev, mhws['duration'][ev], width=0.6, edgecolor=(1,0.,0.), \
+        color='none')
+plt.xlim(0, mhws['n_events'])
+plt.ylabel('[days]')
+plt.title('Duration')
+# Maximum intensity
+plt.subplot(2,2,2)
+evMax = np.argmax(mhws['intensity_max'])
+plt.bar(range(mhws['n_events']), mhws['intensity_max'], width=0.6, \
+        color=(0.7,0.7,0.7))
+plt.bar(evMax, mhws['intensity_max'][evMax], width=0.6, color=(1,0.5,0.5))
+plt.bar(ev, mhws['intensity_max'][ev], width=0.6, edgecolor=(1,0.,0.), \
+        color='none')
+plt.xlim(0, mhws['n_events'])
+plt.ylabel(r'[$^\circ$C]')
+plt.title('Maximum Intensity')
+# Mean intensity
+plt.subplot(2,2,4)
+evMax = np.argmax(mhws['intensity_mean'])
+plt.bar(range(mhws['n_events']), mhws['intensity_mean'], width=0.6, \
+        color=(0.7,0.7,0.7))
+plt.bar(evMax, mhws['intensity_mean'][evMax], width=0.6, color=(1,0.5,0.5))
+plt.bar(ev, mhws['intensity_mean'][ev], width=0.6, edgecolor=(1,0.,0.), \
+        color='none')
+plt.xlim(0, mhws['n_events'])
+plt.title('Mean Intensity')
+plt.ylabel(r'[$^\circ$C]')
+plt.xlabel('MHW event number')
+# Cumulative intensity
+plt.subplot(2,2,3)
+evMax = np.argmax(mhws['intensity_cumulative'])
+plt.bar(range(mhws['n_events']), mhws['intensity_cumulative'], width=0.6, \
+        color=(0.7,0.7,0.7))
+plt.bar(evMax, mhws['intensity_cumulative'][evMax], width=0.6, color=(1,0.5,0.5))
+plt.bar(ev, mhws['intensity_cumulative'][ev], width=0.6, edgecolor=(1,0.,0.), \
+        color='none')
+plt.xlim(0, mhws['n_events'])
+plt.title(r'Cumulative Intensity')
+plt.ylabel(r'[$^\circ$C$\times$days]')
+plt.xlabel('MHW event number')
+
+ +
+
+
+ +
+
+ + +
Out[12]:
+ + +
+
<matplotlib.text.Text at 0x61d7510>
+
+ +
+ +
+ + +
+ +
+ +
+ +
+
+ +
+
+
+
+
+
+

However, the 2012 NWA event (red outlined bars) is not the highest ranked event (red shaded bars) when sorted according to mean intensity, cumulative intenstiy and duration:

+ +
+
+
+
+
+
In [13]:
+
+
+
rank, returnPeriod = mhw.rank(t, mhws)
+print "The 2012 NWA event is ranked number " \
+        + str(rank['duration'][ev]) + " by duration"
+print "The 2012 NWA event is ranked number " \
+        + str(rank['intensity_max'][ev]) + " by maximum intensity"
+print "The 2012 NWA event is ranked number " \
+        + str(rank['intensity_mean'][ev]) + " by mean intensity"
+print "The 2012 NWA event is ranked number " \
+        + str(rank['intensity_cumulative'][ev]) + " by cumulative intensity"
+
+ +
+
+
+ +
+
+ + +
+
+
The 2012 NWA event is ranked number 4 by duration
+The 2012 NWA event is ranked number 1 by maximum intensity
+The 2012 NWA event is ranked number 6 by mean intensity
+The 2012 NWA event is ranked number 3 by cumulative intensity
+
+
+
+ +
+
+ +
+
+
+
+
+
+

Case study #3: 2003 Mediterranean event

We can also have a look at the 2003 Mediterranean (Med) event. Let's load a daily time series of SST from the Med just south of France (9$^\circ$E, 43.5$^\circ$N) from the same data set as above and repeat the analysis:

+ +
+
+
+
+
+
In [14]:
+
+
+
# Load Mediterranean SST time series
+sst = np.loadtxt('data/sst_Med.csv', delimiter=',')
+
+# Detect MHW events
+mhws, clim = mhw.detect(t, sst)
+
+# Find largest event
+ev = np.argmax(mhws['intensity_max'])
+print 'Maximum intensity:', mhws['intensity_max'][ev], 'deg. C'
+print 'Average intensity:', mhws['intensity_mean'][ev], 'deg. C'
+print 'Cumulative intensity:', mhws['intensity_cumulative'][ev], 'deg. C-days'
+print 'Duration:', mhws['duration'][ev], 'days'
+print 'Start date:', mhws['date_start'][ev].strftime("%d %B %Y")
+print 'End date:', mhws['date_end'][ev].strftime("%d %B %Y")
+
+ +
+
+
+ +
+
+ + +
+
+
Maximum intensity: 5.04771933977 deg. C
+Average intensity: 3.8731899862 deg. C
+Cumulative intensity: 34.8587098758 deg. C-days
+Duration: 9 days
+Start date: 26 June 2008
+End date: 04 July 2008
+
+
+
+ +
+
+ +
+
+
+
+
+
+

We are looking for the 2003 Med event but the largest event on record, according to maximum intensity, occurred in 2008. However, the 2003 Med event is the largest according to mean intensity:

+ +
+
+
+
+
+
In [15]:
+
+
+
# Find largest event (by mean intensity)
+ev = np.argmax(mhws['intensity_mean'])
+print 'Maximum intensity:', mhws['intensity_max'][ev], 'deg. C'
+print 'Average intensity:', mhws['intensity_mean'][ev], 'deg. C'
+print 'Cumulative intensity:', mhws['intensity_cumulative'][ev], 'deg. C-days'
+print 'Duration:', mhws['duration'][ev], 'days'
+print 'Start date:', mhws['date_start'][ev].strftime("%d %B %Y")
+print 'End date:', mhws['date_end'][ev].strftime("%d %B %Y")
+
+ +
+
+
+ +
+
+ + +
+
+
Maximum intensity: 5.02208493174 deg. C
+Average intensity: 4.06091222595 deg. C
+Cumulative intensity: 121.827366778 deg. C-days
+Duration: 30 days
+Start date: 02 June 2003
+End date: 01 July 2003
+
+
+
+ +
+
+ +
+
+
+
+
+
+

And a time series plot shows it clearly to be a large event:

+ +
+
+
+
+
+
In [16]:
+
+
+
plt.figure(figsize=(14,10))
+plt.subplot(2,1,1)
+# Plot SST, seasonal cycle, and threshold
+plt.plot(dates, sst, 'k-')
+plt.plot(dates, clim['thresh'], 'g-')
+plt.plot(dates, clim['seas'], 'b-')
+plt.title('SST (black), seasonal climatology (blue), threshold (green), \
+        detected MHW events (shading)')
+plt.xlim(t[0], t[-1])
+plt.ylim(sst.min()-0.5, sst.max()+0.5)
+plt.ylabel(r'SST [$^\circ$C]')
+plt.subplot(2,1,2)
+# Find indices for all ten MHWs before and after event of interest and shade accordingly
+for ev0 in np.arange(ev-10, ev+11, 1):
+    t1 = np.where(t==mhws['time_start'][ev0])[0][0]
+    t2 = np.where(t==mhws['time_end'][ev0])[0][0]
+    plt.fill_between(dates[t1:t2+1], sst[t1:t2+1], clim['thresh'][t1:t2+1], \
+                     color=(1,0.6,0.5))
+# Find indices for MHW of interest (2003 Med event) and shade accordingly
+t1 = np.where(t==mhws['time_start'][ev])[0][0]
+t2 = np.where(t==mhws['time_end'][ev])[0][0]
+plt.fill_between(dates[t1:t2+1], sst[t1:t2+1], clim['thresh'][t1:t2+1], color='r')
+# Plot SST, seasonal cycle, threshold, shade MHWs with main event in red
+plt.plot(dates, sst, 'k-', linewidth=2)
+plt.plot(dates, clim['thresh'], 'g-', linewidth=2)
+plt.plot(dates, clim['seas'], 'b-', linewidth=2)
+plt.title('SST (black), seasonal climatology (blue), threshold (green), \
+        detected MHW events (shading)')
+plt.xlim(mhws['time_start'][ev]-150, mhws['time_end'][ev]+150)
+plt.ylim(clim['seas'].min() - 1, clim['seas'].max()\
+         + mhws['intensity_max'][ev] + 0.5)
+plt.ylabel(r'SST [$^\circ$C]')
+
+ +
+
+
+ +
+
+ + +
Out[16]:
+ + +
+
<matplotlib.text.Text at 0x67ab450>
+
+ +
+ +
+ + +
+ +
+ +
+ +
+
+ +
+
+
+
+
+
+

And we can see where this event (red outlined bars) fits amongst all other detected events:

+ +
+
+
+
+
+
In [17]:
+
+
+
plt.figure(figsize=(15,7))
+# Duration
+plt.subplot(2,2,1)
+evMax = np.argmax(mhws['duration'])
+plt.bar(range(mhws['n_events']), mhws['duration'], width=0.6, \
+        color=(0.7,0.7,0.7))
+plt.bar(evMax, mhws['duration'][evMax], width=0.6, color=(1,0.5,0.5))
+plt.bar(ev, mhws['duration'][ev], width=0.6, edgecolor=(1,0.,0.), \
+        color='none')
+plt.xlim(0, mhws['n_events'])
+plt.ylabel('[days]')
+plt.title('Duration')
+# Maximum intensity
+plt.subplot(2,2,2)
+evMax = np.argmax(mhws['intensity_max'])
+plt.bar(range(mhws['n_events']), mhws['intensity_max'], width=0.6, \
+        color=(0.7,0.7,0.7))
+plt.bar(evMax, mhws['intensity_max'][evMax], width=0.6, color=(1,0.5,0.5))
+plt.bar(ev, mhws['intensity_max'][ev], width=0.6, edgecolor=(1,0.,0.), \
+        color='none')
+plt.xlim(0, mhws['n_events'])
+plt.ylabel(r'[$^\circ$C]')
+plt.title('Maximum Intensity')
+# Mean intensity
+plt.subplot(2,2,4)
+evMax = np.argmax(mhws['intensity_mean'])
+plt.bar(range(mhws['n_events']), mhws['intensity_mean'], width=0.6, \
+        color=(0.7,0.7,0.7))
+plt.bar(evMax, mhws['intensity_mean'][evMax], width=0.6, color=(1,0.5,0.5))
+plt.bar(ev, mhws['intensity_mean'][ev], width=0.6, edgecolor=(1,0.,0.), \
+        color='none')
+plt.xlim(0, mhws['n_events'])
+plt.title('Mean Intensity')
+plt.ylabel(r'[$^\circ$C]')
+plt.xlabel('MHW event number')
+# Cumulative intensity
+plt.subplot(2,2,3)
+evMax = np.argmax(mhws['intensity_cumulative'])
+plt.bar(range(mhws['n_events']), mhws['intensity_cumulative'], width=0.6, \
+        color=(0.7,0.7,0.7))
+plt.bar(evMax, mhws['intensity_cumulative'][evMax], width=0.6, color=(1,0.5,0.5))
+plt.bar(ev, mhws['intensity_cumulative'][ev], width=0.6, edgecolor=(1,0.,0.), \
+        color='none')
+plt.xlim(0, mhws['n_events'])
+plt.title(r'Cumulative Intensity')
+plt.ylabel(r'[$^\circ$C$\times$days]')
+plt.xlabel('MHW event number')
+
+ +
+
+
+ +
+
+ + +
Out[17]:
+ + +
+
<matplotlib.text.Text at 0x7ac2890>
+
+ +
+ +
+ + +
+ +
+ +
+ +
+
+ +
+
+
+
In [18]:
+
+
+
rank, returnPeriod = mhw.rank(t, mhws)
+print "The 2012 NWA event is ranked number " \
+        + str(rank['duration'][ev]) + " by duration"
+print "The 2012 NWA event is ranked number " \
+        + str(rank['intensity_max'][ev]) + " by maximum intensity"
+print "The 2012 NWA event is ranked number " \
+        + str(rank['intensity_mean'][ev]) + " by mean intensity"
+print "The 2012 NWA event is ranked number " \
+        + str(rank['intensity_cumulative'][ev]) + " by cumulative intensity"
+
+ +
+
+
+ +
+
+ + +
+
+
The 2012 NWA event is ranked number 5 by duration
+The 2012 NWA event is ranked number 2 by maximum intensity
+The 2012 NWA event is ranked number 1 by mean intensity
+The 2012 NWA event is ranked number 2 by cumulative intensity
+
+
+
+ +
+
+ +
+
+
+
+
+
+

We can even look at the return periods for events with those properties:

+ +
+
+
+
+
+
In [19]:
+
+
+
print "The return period for an event with this duration was " \
+        + str(returnPeriod['duration'][ev]) + " years"
+print "The return period for an event with this maximum intensity was " \
+        + str(returnPeriod['intensity_max'][ev]) + " years"
+print "The return period for an event with this mean intensity was " \
+        + str(returnPeriod['intensity_mean'][ev]) + " years"
+print "The return period for an event with this cumulative intensity was " \
+        + str(returnPeriod['intensity_cumulative'][ev]) + " years"
+
+ +
+
+
+ +
+
+ + +
+
+
The return period for an event with this duration was 6.79986310746 years
+The return period for an event with this maximum intensity was 16.9996577687 years
+The return period for an event with this mean intensity was 33.9993155373 years
+The return period for an event with this cumulative intensity was 16.9996577687 years
+
+
+
+ +
+
+ +
+
+
+
+
+
+

Block-averaged Marine Heatwave properties

+
+
+
+
+
+
+
+
+

The marineHeatWaves (mhw) module also consists of functions to calculate the average of MHW properties over blocks in time (e.g., annually, decadally). The block-averaging function (blockAverage) takes as input a set of detected MHWs (i.e., the output from detect, the detection function described above) and outputs the MHW properties averaged over the specified block-length. This output can then be passed through the meanTrend function in order to calculate the time-mean and linear trend of the MHW properties over the measurement period.

+

Let's start by applying the block-averaging function to the Mediterranean MHWs which are stored in the variable mhws, using the default block length of 1 year (i.e., annual averages):

+ +
+
+
+
+
+
In [20]:
+
+
+
mhwBlock = mhw.blockAverage(t, mhws)
+
+ +
+
+
+ +
+
+
+
+
+
+

The variable mhwBlock has a set of keys which are time series of the MHW properties over the blocks. The central year of the blocks are stored in the key years_centre so we can look at, as an example, time series of MHW counts in each year and the average maximum intensity in each year:

+ +
+
+
+
+
+
In [21]:
+
+
+
plt.figure(figsize=(14,4))
+plt.subplot(1,2,1)
+plt.plot(mhwBlock['years_centre'], mhwBlock['count'], 'k-o')
+plt.ylim(0,9)
+plt.ylabel('[count]')
+plt.title('Number of MHWs by year')
+plt.subplot(1,2,2)
+plt.plot(mhwBlock['years_centre'], mhwBlock['intensity_max'], 'k-o')
+plt.ylabel(r'[$^\circ$C]')
+plt.title('Average MHW maximum intensity by year')
+
+ +
+
+
+ +
+
+ + +
Out[21]:
+ + +
+
<matplotlib.text.Text at 0x7830610>
+
+ +
+ +
+ + +
+ +
+ +
+ +
+
+ +
+
+
+
+
+
+

There certainly looks like a positive trend in the annual number of MHWs and possibly in the maximum intensity as well. We can calculate the mean and trend of the MHW properties using the meanTrend function:

+ +
+
+
+
+
+
In [22]:
+
+
+
mean, trend, dtrend = mhw.meanTrend(mhwBlock)
+print "There are on average " + str(mean['count']) + " MHWs in each year, \n \
+with a linear trend of " + str(10*trend['count']) + " MHW events per decade \n \
+This trend is statistically significant (p<0.05): " \
++ str(np.abs(trend['count']) > dtrend['count']) + "\n"
+
+print "The average maximum intensity is " + str(mean['intensity_max']) + " deg. C, \n \
+with a linear trend of " + str(10*trend['intensity_max']) + " deg. C per decade \n \
+This trend is statistically significant (p<0.05): " \
++ str(np.abs(trend['intensity_max']) > dtrend['intensity_max'])
+
+ +
+
+
+ +
+
+ + +
+
+
There are on average 2.12121212121 MHWs in each year, 
+ with a linear trend of 0.935828877005 MHW events per decade 
+ This trend is statistically significant (p<0.05): True
+
+The average maximum intensity is 2.5632717716 deg. C, 
+ with a linear trend of 0.200430231669 deg. C per decade 
+ This trend is statistically significant (p<0.05): False
+
+
+
+ +
+
+ +
+
+
+ + diff --git a/setup.py b/setup.py index 1ec52b2..3cb45b0 100644 --- a/setup.py +++ b/setup.py @@ -2,7 +2,7 @@ from distutils.core import setup setup(name='marineHeatWaves', - version='0.10', + version='0.11', author = "Eric C. J. Oliver", author_email = "eric.oliver@utas.edu.au", description = ("A set of functions which implement the Marine Heatwave definition of Hobday et al. (2015)"),