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14_Band-limited-Interpolation-of-Radiation-Measurements.py
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Safecast : Band-limited interpolation of radiation measurements in Fukushima\n",
"============================================================================\n",
"\n",
"Summary\n",
"-------\n",
"\n",
"In this notebook, we'll use radiation data from around the Fukushima Dai-ichi power plant in Japan to demonstrate some basic band-limited interpolation techniques.\n",
"\n",
"__Disclaimer__: This notebook is fairly heavy to run in terms of memory usage. A machine with at least 8GB of RAM is recommended.\n",
"\n",
"History\n",
"-------\n",
"\n",
"When a tsunami hit the coast of Japan on March 11 2011, in addition to the terrible devastation brought in by the tidal wave, another disaster unfolded, the infamous nuclear disaster of the Fukushima Dai-ichi nuclear power station. Under the assault of waves over 14 meters, three nuclear reactors underwent meltdown, explosions, and are to this day not yet under control.\n",
"\n",
"![Explosion](http://i.telegraph.co.uk/multimedia/archive/01847/smoke_1847738c.jpg)\n",
"\n",
"A consequence of the accident was the release of important quantities of radioactive material into the environment. In spite of the potential danger faced by the population, virtually no information concerning the levels of radioactive contamination was released by either the power utility company or the governement of Japan. It was quickly clear that the reason was not only the reluctance of official bodies to release the information, but that for the most part the information did not exist in the first place.\n",
"\n",
"Facing this situation, [Safecast](http://blog.safecast.org/), an international group of concerned citizens, quickly formed after the disaster. To remediate to the lack of the data, the group decided to build sensor themselves and lend them to volunteers that could in turn take the measurements and share them back with the community through a common database.\n",
"\n",
"<img src='http://i.imgur.com/wfa34yD.jpg' width=500>\n",
"\n",
"To streamline the collection of data, a new type of mobile sensor was developped with the help of [Tokyo Hackerspace](http://tokyohackerspace.org/), the bGeigie. The bGeigie includes an Arduino for the brains, a GPS, an SD card, and a Geiger tube (with high voltage). The dose rate is measurement using the Geigier counter, tagged with time and GPS coordinates and recorded to the SD card. The device straps to the outside of a car (or bike, or backpack, etc) and automatically takes a measurement every five seconds. This allows for extremely efficient collection of measurements.\n",
"\n",
"<img src='http://i.imgur.com/EeRcK0K.jpg' width=400> <img src='http://i.imgur.com/FLNtxDZ.jpg' width=200>\n",
"\n",
"This strategy allowed to gather data at a very high rate and today most of Japan, as well as some other areas around the world have been covered. The whole dataset can be [downloaded](https://api.safecast.org/system/measurements.csv) or visualized on [maps](http://safecast.org/tilemap). More than 19 million individual measurements have been collected so far.\n",
"\n",
"<a href='http://safecast.org/tilemap'>\n",
"<img src='https://i.imgur.com/uTvHT0h.png' width=800>\n",
"</a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Band-limited interpolation\n",
"--------------------------\n",
"\n",
"Interpolation deals with the reconstruction of a continuous field from a set of discrete measurements. Band-limited refers to the case where we make the extra assumption that the field we wish to reconstruct does not have any high-frequency. \n",
"\n",
"As one might expect, this requirement can be expressed in the language of Fourier analysis. But first, let's make the extra two following assumptions.\n",
"\n",
"1. We are only interested in a finite interval $[x_1,x_2]$.\n",
"2. The function is periodic with period $T = x_2 - x_1$.\n",
"\n",
"Then, the Fourier transform of the function will be zero everywhere, except at integer locations (this can be understood by constructing the function as the convolution of a pulse train with the windowed interval, and then applying the convolution theorem). Thus, we only need to compute the Fourier transform at integer frequencies. (This is in fact a [Fourier series](https://en.wikipedia.org/wiki/Fourier_series) and is the original work by [Joseph Fourier](https://en.wikipedia.org/wiki/Jean-Baptiste_Joseph_Fourier), but we will not go into details here.)\n",
"\n",
"Adding the band-limitdness assumption to this, we can write the Fourier expansion of the function as a finite sum\n",
"$$\n",
"f(x) = \\sum_{k=-M}^M c_k e^{j2\\pi \\frac{k x}{T}}, \\quad t\\in \\mathbb{R}.\n",
"$$\n",
"\n",
"In this notebook, we will first study interpolation of 1D signals to understand the technique. Then we will apply the same technique to the 2D radiation field using the Safecast dataset."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Band-limited interpolation of 1D signals\n",
"----------------------------------------\n",
"\n",
"Let's assume we have a number of measurements from a 1D field.\n",
"\n",
"$$\n",
"\\{(x_i,z_i)\\}_{i=0}^{N-1}\n",
"$$\n",
"\n",
"such that $z_i = f(x_i)$ and $f(x)$ is a bandlimited function as described above. This means that the following equations are satisfied.\n",
"\n",
"$$\n",
"z_i = \\sum_{k=-M}^M c_k\\, e^{j2\\pi\\frac{k x_i}{T}},\\ i=0,\\ldots,N-1.\n",
"$$\n",
"\n",
"This equation can be rewritten in matrix form as\n",
"\n",
"$$\n",
"F\\mathbf{c} = \\mathbf{z},\n",
"$$\n",
"\n",
"where $\\{F\\}_{ik} = e^{j2\\pi\\frac{x_i k}{T}}$, $\\mathbf{c}=[c_{-M},\\ldots,c_{M}]^T$ is a vector containing the Fourier coefficients, and $\\mathbf{z}=[z_0,\\ldots,z_{N-1}]^T$ are the measurements.\n",
"\n",
"Note that we keep $i$ from $0$ to $N-1$, and $k$ from $-M$ to $M$, as in the initial sum. In the matrix notation, this simply means that the upper left entry of the matrix is $F_{0,-M}$.\n",
"\n",
"Assuming that $N \\geq 2M+1$, this system can be solved in the least-square sense to give an approximation of the Fourier coefficients\n",
"\n",
"$$\n",
"\\hat{\\mathbf{c}} = (F^TF)^{-1}F^Tz.\n",
"$$\n",
"\n",
"Given the estimated Fourier coefficients, it is now possible to estimate the field on different set of points, e.g. a regular grid. Let $\\tilde{x}_i = i\\frac{T}{L}$, the regularly spaced grid. Then the function at these points is\n",
"\n",
"$$\n",
"\\tilde{\\mathbf{z}} = \\tilde{F}\\hat{c},\n",
"$$\n",
"\n",
"where $\\{\\tilde{F}\\}_{ik} = e^{j2\\pi\\frac{\\tilde{x}_i k}{T}}$.\n",
"\n",
"Let's now put this in practice."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"# import pylab and make figure size something nice for display\n",
"%pylab inline\n",
"figsize(8,6)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We start by defining a function that will take care of the interpolation as described above. It takes as arguments the measurements, the interval, the maximum order of the Fourier coefficients, and optionally a grid step size (and a conditional argument to use a window function, but more about this later)."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def BL_interp_1D(x, z, T, order, grid_step=0.01, win=True):\n",
" \"\"\"\n",
" Band-limited interpolation of 1D functions\n",
" \"\"\"\n",
" \n",
" # Create Fourier order vector\n",
" k = expand_dims(arange(-order, order+1), 0)\n",
" \n",
" # construct the Fourier matrix\n",
" F = exp(2j*pi*x*k/(T[1]-T[0]))\n",
" \n",
" # Least-square projection (alternatively numpy.linalg.lstsq can be used)\n",
" C = dot(dot(linalg.inv(dot(F.T,F)), F.T), z)\n",
" \n",
" # create new evenly spaced grid\n",
" xg = expand_dims(arange(T[0], T[1], grid_step), 1)\n",
" \n",
" # window the Fourier coefficients if requested\n",
" if (win):\n",
" C *= expand_dims(hanning(2*order+1), 1)\n",
" \n",
" zg = dot(exp(2j*pi*xg*k/(T[1]-T[0])), C)\n",
" \n",
" return zg, xg, C, k"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, we will take randomly spaced samples from a the band-limited function $f_{BL}(x) = 2\\sin(2\\pi x) - 4\\cos(2\\pi 4 x)$, and try to interpolate the function on a new grid."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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05Ek2TZlidCgOY8tPu2Ag596JUabHsonIQBHZJSK7Ll26ZMNT2947EQcYvmQv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\nzpIkFcZwliSpMIazJEmFMZwlSSrM/wPU2qhYcgAfwgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f51dffeddd8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# define the f_BL as a function for convenience\n",
"def f_BL(x):\n",
" return 2*np.sin(2*pi*1*x) - 4*np.cos(2*pi*4*x)\n",
"\n",
"# Take a random set of measurements on [0,2\\pi]\n",
"T = [0, 1]\n",
"order = 6\n",
"\n",
"x = (T[1]-T[0])*random.random((100,1))+T[0]\n",
"z = f_BL(x)\n",
"\n",
"zp1, xp1, C1, k1 = BL_interp_1D(x, z, T, order, win=False)\n",
"\n",
"subplot(2,1,1)\n",
"plot(xp1, real(zp1), 'r-', xp1, f_BL(xp1), 'k--', x, z, 'o')\n",
"title('Time Domain')\n",
"legend(('Interpolated', 'Original','Measurements'))\n",
"\n",
"subplot(2,1,2)\n",
"stem(k1.T, abs(C1))\n",
"title('Fourier coefficients magnitude')\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We notice that we recover the exact original field. This happens because the field we chose perfectly match our band-limited hypothesis. One could ask, what if the field is not band-limited ? Can we do anything ?\n",
"\n",
"Let's try with a non band-limited function. We take the function $f_2(x)=(|x|-0.5)^2$ for $x\\in[-0.5,0.5]$ and periodized with period $T=1$. This function is continuous, but not differentiable. It has a sharp angle at $x=0$ and is therefore not band-limited."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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9u5M5rrs+U7l+9UjYeRT7/ZjqwZ+knQyc7bbcAkj19wSqmur8uwtYBkSXID5j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\nbs15H5od55G2WQvNmto7quV2Iu9Ds+MctM1aaN2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"text/plain": [
"<matplotlib.figure.Figure at 0x7f51ddd62e10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def f2(x):\n",
" return (abs(x)-0.5)**2\n",
"\n",
"T = [-0.5, 0.5]\n",
"order = 10\n",
"\n",
"x = (T[1]-T[0])*random.random((100,1))+T[0]\n",
"z = f2(x)\n",
"\n",
"# compute BL interpolation\n",
"zp1, xp1, C1, k1 = BL_interp_1D(x, z, T, order, win=False)\n",
"\n",
"# plot the result\n",
"subplot(2,1,1)\n",
"plot(xp1, real(zp1), 'r-', xp1, f2(xp1), 'k--', x, z, 'o')\n",
"xlim([-0.5,0.5])\n",
"title('Time Domain')\n",
"legend(('Interpolated', 'Original','Measurements'))\n",
"\n",
"subplot(2,1,2)\n",
"stem(k1.T, abs(C1), 'k')\n",
"title('Fourier coefficients magnitude')\n",
"\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The function $f_2(x)$, although continuous, is not differentiable around zero. This means that it is not band-limited. We can understand it in the following way. To approximate the sharp edge at zero with the smooth sine and cosine of the Fourier expansion, an infinite number of coefficients is necessary. However, we see that except around zero, where the sharp angle is smoothed out, our approximation is still excellent.\n",
"\n",
"What if we deal with a discontinuous function ? To test this we will use $f_3(x) = x^2$ for $x\\in[0,1)$ and periodized with $T=1$."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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V8oQrV65QcuFCvAYNYmK5ciRcOodPmUoZHuNr8854Ccz777eCb79+Vst59WoY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\nS5JUEwZtSZJqwqAtSVJN/H8SJAF7bvLWMAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f51e0006be0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# we use fractional part function modf to compactly write f_3\n",
"def f3(x):\n",
" return (x-floor(x))**2\n",
"\n",
"T = [-0.5, 0.5]\n",
"order = 10\n",
"\n",
"x = (T[1]-T[0])*random.random((100,1))+T[0]\n",
"z = f3(x)\n",
"\n",
"# compute BL interpolation\n",
"zp1, xp1, C1, k1 = BL_interp_1D(x, z, T, order, win=False)\n",
"\n",
"# plot the result\n",
"subplot(2,1,1)\n",
"plot(xp1, real(zp1), 'r-', xp1, f3(xp1), 'k--', x, z, 'o')\n",
"xlim([-0.5,0.5])\n",
"title('Time Domain')\n",
"legend(('Interpolated', 'Groundtruth','Measurements'))\n",
"\n",
"subplot(2,1,2)\n",
"stem(k1.T, abs(C1), 'k')\n",
"title('Fourier coefficients magnitude')\n",
"\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that in this case, the discontinuity requires much more high frequency coefficients to be well approximated (in fact, one can show that the Fourier coefficients only decrease as $\\sim\\frac{1}{k}$). One way to understand what is happening is to see the band-limited approximation as applying a rectangular window in the frequency domain\n",
"\n",
"$$\n",
"\\hat{c}_k = w_k c_k\n",
"$$\n",
"\n",
"with $w_k = 1$ if $|k| \\leq M$, and zero otherwise. By one of the fundamental properties of the Fourier transform, we know that the resulting time domain signal will be convolved with the Fourier expansion of the rectangular window, i.e. the sinc function. Which explains the wiggles we see.\n",
"\n",
"A solution to this problem is to apply a different window function that is better behaved in the time domain. For example, the [Hann window](https://en.wikipedia.org/wiki/Hann_function). Essentially, we are trading off resolution for smoothness. For a detailed discussion of window functions, one can refer to the [wikipedia entry](https://en.wikipedia.org/wiki/Window_function) on the subject.\n",
"\n",
"Let's see now what we obtain using the window function."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Wrfnwww/jSnnGDuOHeniAs7MEbSFyAVuC9iXAy+p9CSC5BK0vkWBoXGt92fL1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\n4MDcuXM5d+4cU6ZMycRWiieJf0AQjaZ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xDqKWs2VcM2w5R58t4+jz4zI+QVWbVVUoLpO2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\nMcb4hCVtY4wxxif+H/pEh/YhsgIPAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f51e0006588>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# compute BL interpolation\n",
"zp2, xp2, C2, k2 = BL_interp_1D(x, z, T, order, win=True)\n",
"\n",
"# plot the result\n",
"subplot(2,1,1)\n",
"plot(xp1, real(zp1), 'r-', xp2, real(zp2), 'k-', xp1, f3(xp1), 'k--', x, z, 'o')\n",
"xlim([-0.5,0.5])\n",
"title('Time Domain')\n",
"legend(('No windowing', 'Windowing','Groundtruth','Measurements'))\n",
"\n",
"subplot(2,1,2)\n",
"markerline, stemlines, baseline = stem(k1.T, abs(C1), 'k')\n",
"setp(markerline, 'markerfacecolor', 'k')\n",
"setp(baseline, 'color','k')\n",
"markerline, stemlines, baseline = stem(k2.T, abs(C2), 'k')\n",
"setp(markerline, 'markerfacecolor', 'r')\n",
"setp(baseline, 'color','k')\n",
"legend(('Original spectrum', 'Windowed spectrum'))\n",
"title('Fourier coefficients magnitude')\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We observe that we lost some sharpness at the discontinuity by applying the window. However, we gained a lot of smoothness and far better approximation in the rest of the signal."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Band-limited interpolation of 2D signals\n",
"----------------------------------------\n",
"\n",
"The principles we will apply here are identical to 1D signals. The only difficulty is to write our 2D equation in matrix form. However, as we will see, python offers facilities for this.\n",
"\n",
"Let's assume we have now measurements from a 2D field,\n",
"\n",
"$$\n",
"\\{(x_i,y_i,z_i)\\}_{i=0}^{N-1}\n",
"$$\n",
"\n",
"where $z_i = f(x_i,y_i)$. Assuming $f(x,y)$ is a band-limited function, we can write each measaurement as a Fourier expansion\n",
"\n",
"$$\n",
"z_i = f(x,y) = \\sum_{k=-M}^M\\sum_{l=-M}^M c_{kl}\\, e^{j2\\pi\\left(\\frac{x_i k}{T_x}+\\frac{y_i l}{T_y}\\right)},\n",
"$$\n",
"\n",
"where again we assumed $f(x,y)$ is periodic with periods $T_x$ and $T_y$ in the $x$ and $y$ directions, respectively. We can again rewrite this in matrix form $F\\mathbf{c} = \\mathbf{z}$. This is possible by linearizing 2D indices $k,l$ in the following way for example $\\mathbf{c}_{k+(2M+1)l} = c_{kl}$ and $\\{F\\}_{i,k+(2M+1)l} = e^{j2\\pi\\left(\\frac{x_i k}{T_x}+\\frac{y_i l}{T_y}\\right)}$, and $\\mathbf{z}$ as before (we assumed here that we shift $k$ and $l$ to be positive). In practice, we'll use python built-in routines to do this task (so exact order may vary), in particular check the [`meshgrid`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.meshgrid.html) and [`reshape`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.reshape.html) routines. Thus, if we are careful about the reordering of the coefficients, we can re-use the exact same technique as in the 1D case!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Interpolate Safecast data around Fukushima Dai-ichi power plant\n",
"---------------------------------------------------------------\n",
"\n",
"We start by importing the data. Be careful, if the data is not available locally, a 2 GB file has to be downloaded and processed. This can take some time.\n",
"\n",
"For convenience, we restrict the Safecast dataset to measurements made around the stricken nuclear power plant. We also remove very large measurements as they tend to be very spotty and throw off the interpolation (they have very large bandwidth). This kind of preprocessing is typical of real-world datasets and needs to be adjusted on a case by case basis."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of measurements: 941573\n"
]
}
],
"source": [
"import pandas as pd\n",
"import datetime as dt\n",
"import os\n",
"\n",
"# Limit data to use in space and time\n",
"lat_min, lon_min, lat_max, lon_max = 37.037571, 139.540087, 37.856355, 141.050707 # Fukushima area only\n",
"dr = ['2011-03-11', '2012-03-11'] # Limit time to first year after accident\n",
"Value_max = 2500 # Discard very large samples as they tend to throw off interpolation\n",
"\n",
"# data filename\n",
"filename = 'Safecast_data.txt'\n",
"\n",
"# If the data file do not exist, we just grab all the data from Safecast's website\n",
"if (not os.path.isfile(filename)):\n",
" \n",
" local_full_dataset = 'measurements.csv'\n",
" \n",
" # if the file is not locally present, download from Safecast website\n",
" if (not os.path.isfile(local_full_dataset)):\n",
" df = pd.read_csv('https://api.safecast.org/system/measurements.csv', parse_dates=True, index_col=0)\n",
" else:\n",
" df = pd.read_csv(local_full_dataset, parse_dates=True, index_col=0)\n",
" \n",
" # sort the index to be ordered chronologically\n",
" df.sort_index(inplace=True)\n",
" \n",
" # Select the measurements in that space-time interval\n",
" map_space = logical_and(logical_and(df.Latitude > lat_min, df.Latitude < lat_max), logical_and(df.Longitude > lon_min, df.Longitude < lon_max))\n",
" map_mag = logical_and(df.Value > 0, df.Value < Value_max)\n",
" df_fuku = df[['Longitude','Latitude','Value']][logical_and(map_space, map_mag)][dr[0]:dr[1]]\n",
" \n",
" # save locally for further use\n",
" df_fuku.to_csv(filename)\n",
"\n",
"else:\n",
" df_fuku = pd.read_csv(filename, error_bad_lines=False)\n",
" \n",
" \n",
"print('Number of measurements: ', len(df_fuku))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Note__: The computational burden of the notebook can be decreased by subsampling the vector `df_fuku` here (only keeping one out of every $x$ entries for example).\n",
"\n",
"Now, let's take a look at the data we have at hand. Since they were taken with a car, we expect the measurements to line up into trajectories following the road network."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<class 'pandas.core.frame.DataFrame'>\n"
]
},
{
"data": {
"image/png": 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JrNvnKZ87boR1bdFOyytMg2jeAA6MuD/B+j+XnVJnBSnAmp/X4hWkx7Y/ipM7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ZOPrHSRzYfTTEGQX3aTsi7IViBmveuTFUtZQQAYQI6P3AxDzPG/IUKzNmMnUKBKUrx2LOzlew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\nCGMqEAgEAoGf/B/qjAnj8ZzsuQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f51ddb38cc0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ax = subplot(111)\n",
"print(type(df_fuku))\n",
"plt.scatter(df_fuku.Longitude, df_fuku.Latitude, c=df_fuku.Value, marker='.', edgecolor='none')\n",
"\n",
"plt.tick_params(\\\n",
" axis='both', # changes apply to the x-axis\n",
" which='both', # both major and minor ticks are affected\n",
" bottom='off', top='off', right='off', left='off', # ticks along the top edge are off\n",
" labelbottom='off',labelleft='off') # labels along the bottom and left edges are off\n",
"\n",
"ax.set_aspect('equal')\n",
"axis('tight')\n",
"\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Interpolation\n",
"\n",
"Let's go into the interpolation of the 2D radiation field. We mentionned earlier that one of the hidden assumption of our model is that the signal is periodic. It is thus possible to see wrap-around artifacts appear in our interpolation. To reduce this, we add an area empty of measurements. Effectively, we fix our interval to start a pre-defined distance from the closest measurement in all direction.\n",
"\n",
"It turns out also that we need to use another dirty trick here in order to get a good interpolation. Real-world measurements are unfortunately subject to noise. Especially low-level radiation data inherently has low signal-to-noise ratio. In addition, our data contains many redundant, or close to redundant points, leading to a poorly condition $F$ matrix. To better conditionned the matrix, a singular value decomposition is used and the singular values lower than some threshold are discarded. This allows to decrease the [condition number](https://en.wikipedia.org/wiki/Condition_number) of the $F$ matrix and obtain a stable solution to the system. This functionality is luckily implemented in the [`lstsq`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.lstsq.html) function from numpy.\n",
"\n",
"Note that the following piece of code is where the heavy number crunching is done and you'll need a fair amount of RAM to run it."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Choose an order and a padding size for the interpolation\n",
"order = 10\n",
"padding = 0.2 # unit is in degrees for lat/lon\n",
"\n",
"# Recenter the coordinates to start at origin\n",
"x = expand_dims(df_fuku.Longitude - lon_min + padding, 1)\n",
"y = expand_dims(df_fuku.Latitude - lat_min + padding, 1)\n",
"z = expand_dims(df_fuku.Value, 1)\n",
"\n",
"# The size of the interval to interpolate\n",
"Tx = x.max() + padding\n",
"Ty = y.max() + padding\n",
"\n",
"# construct our Fourier order vectors\n",
"k = arange(-order, order+1)\n",
"l = arange(-order, order+1)\n",
"K,L = meshgrid(k,l)\n",
"\n",
"# vectorize\n",
"linK = reshape(K, (1, -1))\n",
"linL = reshape(L, (1, -1))\n",
"\n",
"# make the matrix\n",
"# Note, we rely here on broadcasting by numpy to get the matrix for all pairs of entries from x/linK and y/linL\n",
"F = exp(2j*pi*(x*linK/Tx + y*linL/Ty))/sqrt(Tx*Ty)\n",
"\n",
"# Least-square projection\n",
"C = linalg.lstsq(F, z, 1e-2)[0]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's now take a first look at the spectrum we obtained. We notice the plume like behavior. We also see that the spectrum does not decay gracefully to zero within the order that we chose. To mitigate this, we could either choose a higher order $M$ for the band-limited spectrum, or window the spectrum before reconstruction to smooth things. We will choose the latter here as the addition of more coefficients increases rapidly the amount of memory necessary to solve the least-square problem.\n",
"\n",
"Of course, this also means that we are actually dealing with a field actually not band-limited and our reconstruction will thus be inexact. We hope however that we will get a good idea of the large-scale behavior of the field."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"ax = subplot(1,1,1)\n",
"ax.pcolormesh(K, L, (abs(reshape(C, (2*order+1, 2*order+1)))))\n",
"ax.set_aspect('equal')\n",
"axis([-order, order, -order, order])\n",
"title('Least-square projection of Band-limited spectrum')\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now compute the value of our interpolation on a fine regularly spaced grid over the area. We use the same type of vectorization to go from the 2D representation to our matrix notation described above."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Pick the spacing of the grid\n",
"step = 0.005\n",
"\n",
"# regularly spaced grid\n",
"xg = arange(0, Tx, step)\n",
"yg = arange(0, Ty, step)\n",
"\n",
"# vectorize\n",
"Xg, Yg = meshgrid(xg, yg)\n",
"linXg = reshape(Xg, (1, -1)).T\n",
"linYg = reshape(Yg, (1, -1)).T\n",
"\n",
"# 2D Hann window\n",
"W = expand_dims(hanning(2*order+1), 1)\n",
"W = W*W.T\n",
"Wlin = reshape(W, (1, -1)).T\n",
"\n",
"# Reconstruct after applying the Hann window\n",
"Zprime = dot(exp(2j*pi*(linXg*linK/Tx + linYg*linL/Ty))/sqrt(Tx*Ty), Wlin*C)\n",
"\n",
"# Reshape the result into the original 2D representation\n",
"ZI = real(reshape(Zprime, (len(yg), len(xg))))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now plot the interpolated field. To do so, we also drop the padding area we added previously since it doesn't correspond to anything real. Here we plot in the latitude/longitude domain without any special projection, which means the field is somewhat deformed."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"xmin, xmax = padding/step, (Tx-padding)/step\n",
"ymin, ymax = padding/step, (Ty-padding)/step\n",
"\n",
"Lon = Xg[ymin:ymax,xmin:xmax] + lon_min - padding\n",
"Lat = Yg[ymin:ymax,xmin:xmax] + lat_min - padding\n",
"Field = ZI[ymin:ymax,xmin:xmax]\n",
"\n",
"ax = subplot(1,1,1)\n",
"ax.pcolormesh(Lon, Lat, Field)\n",
"ax.set_aspect('equal')\n",
"axis([Lon.min(), Lon.max(), Lat.min(), Lat.max()])\n",
"title('Reconstructed radiation dose rate field')\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To give a nicer touch to this graph, we will use the `basemap` package from matplotlib to project the reconstructed field on a map. We will also indicate the position of the nuclear power plant, as well as the coast line of Japan.\n",
"\n",
"The `basemap` package is absent from some python distribution (notably Anaconda) and need to be installed by hand. With Anaconda, it is enough to open a terminal and type in the following.\n",
"\n",
" conda install basemap\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Collecting basemap\n",
"\u001b[?25l Downloading https://files.pythonhosted.org/packages/a4/4b/6d0cf7015255fc6c5c2f81875003d8269be3b44fdb273e81b7a2ed68c5da/basemap-1.3.8-cp36-cp36m-manylinux1_x86_64.whl (865kB)\n",
"\u001b[K 100% |████████████████████████████████| 870kB 24.8MB/s ta 0:00:01\n",
"\u001b[?25hCollecting basemap-data<1.4,>=1.3.2 (from basemap)\n",
"\u001b[?25l Downloading https://files.pythonhosted.org/packages/2c/c3/63fdb885308c999206c7a497d79a50891581626da7dc491d432d2732bb46/basemap_data-1.3.2-py2.py3-none-any.whl (30.5MB)\n",
"\u001b[K 100% |████████████████████████████████| 30.5MB 508kB/s eta 0:00:01 10% |███▌ | 3.3MB 60.0MB/s eta 0:00:01 54% |█████████████████▌ | 16.7MB 55.9MB/s eta 0:00:01 61% |███████████████████▉ | 18.9MB 68.9MB/s eta 0:00:01\n",
"\u001b[?25hCollecting pyproj<3.7.0,>=1.9.3; python_version >= \"3.5\" (from basemap)\n",
"\u001b[?25l Downloading https://files.pythonhosted.org/packages/2c/12/7a8cca32506747c05ffd5c6ba556cf8435754af0939906cbcc7fa5802ea3/pyproj-3.0.1.tar.gz (168kB)\n",
"\u001b[K 100% |████████████████████████████████| 174kB 40.4MB/s ta 0:00:01\n",
"\u001b[?25h Installing build dependencies ... \u001b[?25ldone\n",
"\u001b[?25h Complete output from command python setup.py egg_info:\n",
" proj executable not found. Please set the PROJ_DIR variable. For more information see: https://pyproj4.github.io/pyproj/stable/installation.html\n",
" \n",
" ----------------------------------------\n",
"\u001b[31mCommand \"python setup.py egg_info\" failed with error code 1 in /tmp/pip-install-7c6odkii/pyproj/\u001b[0m\n",
"\u001b[33mYou are using pip version 18.0, however version 21.3.1 is available.\n",
"You should consider upgrading via the 'pip install --upgrade pip' command.\u001b[0m\n"
]
}
],
"source": [
"!pip install basemap"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Check Basemap\n"
]
}
],
"source": [
"try: \n",
" from mpl_toolkits.basemap import Basemap\n",
"\n",
" # create figure, axes instances.\n",
" fig = plt.figure()\n",
" ax = fig.add_axes([0.05,0.05,0.9,0.9])\n",
" #\n",
" m = Basemap(llcrnrlon=lon_min, llcrnrlat=lat_min, urcrnrlon=lon_max, urcrnrlat=lat_max,\n",
" rsphere=(6378137.00,6356752.3142),\\\n",
" resolution='l',projection='lcc',\\\n",
" lat_1=lat_min-padding,lat_2=lat_max+padding,lat_0=(lat_max+lat_min)/2.,lon_0=(lon_max+lon_min)/2.)\n",
"\n",
" # draw line around map projection limb.\n",
" m.drawmapboundary(fill_color='0.3')\n",
" m.drawcoastlines(linewidth=2)\n",
" m.drawstates()\n",
" m.drawparallels(arange(37.1,38,0.2),labels=[1,1,0,0], fontsize=14)\n",
" m.drawmeridians(arange(139.5,141.5,0.5),labels=[0,0,1,0], fontsize=14)\n",
"\n",
" # plot sst, then ice with pcolor\n",
" #im1 = m.pcolormesh(Xg+lon_min-padding, Yg+lat_min-padding,ZI,shading='flat',cmap=plt.cm.jet,latlon=True)\n",
"\n",
" nx = int((m.xmax-m.xmin)/50.)+1; ny = int((m.ymax-m.ymin)/50.)+1\n",
" ZIdat = m.transform_scalar(Field, Lon[0],Lat.T[0], nx, ny)\n",
" im1 = m.imshow(ZIdat)\n",
"\n",
" # Add Dai-ichi power station\n",
" daiichi = (37.421463, 141.032556)\n",
" m.scatter(daiichi[1], daiichi[0], latlon=True, marker='*', s=400, color='k')\n",
"\n",
" # add colorbar\n",
" cb = m.colorbar(im1,\"bottom\", size=\"5%\", pad=\"2%\")\n",
" cb.set_label('Radiation dose rate', fontsize=20)\n",
" cb.set_ticks([ZIdat.min(), ZIdat.max()])\n",
" cb.set_ticklabels(('low','high'))\n",
" cb.ax.tick_params(labelsize=20) \n",
"except:\n",
" print('Check Basemap')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To conclude, we can compare our reconstruction to a different interpolation. The interpolation we compare to is done using non-lniear techniques and does not suppose any band-limitedness of the data. It is thus evidently superior. However, we can observe that the band-limited interpolation still gives an excellent first-order approximation.\n",
"\n",
"<img src='http://i.imgur.com/08Aa4KA.png' width=800>"
]
}
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