RNN prediction better than augmented KF, still without rain
[notebooks.git] / ros.ipynb
blobf5bd78f6e85a7b6045ca6c1acdd3ae9018aa7ee8
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4   "metadata": {
5     "colab": {
6       "name": "ros.ipynb",
7       "provenance": [],
8       "collapsed_sections": []
9     },
10     "kernelspec": {
11       "name": "python3",
12       "display_name": "Python 3"
13     },
14     "language_info": {
15       "name": "python"
16     }
17   },
18   "cells": [
19     {
20       "cell_type": "markdown",
21       "metadata": {
22         "id": "K6SPUJOeW0Ns"
23       },
24       "source": [
25         "# Comparison of the fire rate of spread in WRF-SFIRE and FARSITE\n",
26         "## Jan Mandel, instructor of MATH 4770 Math Clinic \n",
27         "## University of Colorado Denver\n",
28         "## December 2021"
29       ]
30     },
31     {
32       "cell_type": "markdown",
33       "metadata": {
34         "id": "AxfvG-MAizyK"
35       },
36       "source": [
37         "## Background"
38       ]
39     },
40     {
41       "cell_type": "markdown",
42       "source": [
43         "### The wind speed vector and the slope vector"
44       ],
45       "metadata": {
46         "id": "DfMzwuZdTvFO"
47       }
48     },
49     {
50       "cell_type": "markdown",
51       "source": [
52         "The wind speed is a vector. We can write the wind vector in Cartesian coordinates as $$\\vec{w}=(w_x,w_y)\\quad \\text{(m/s)}.$$ The $x,y$ axes can be, e.g., east-west and south-north, but that is not important here.\n",
53         "\n",
54         "The slope is also a vector. Denote by $z=z(x,y)$ the terrain height, e.g., above the sea level. The slope vector is the gradient of the terrain height, $$\\vec{s}=\\left(\\frac{\\partial z}{\\partial x},\\frac{\\partial z}{\\partial y}\\right)\\quad\\text{(m/m})$$.\n",
55         "\n",
56         "***Explain how is the slope referred to as $\\tan \\phi = \\|\\vec{s}\\|$. This might be best done with a 3D picture.***"
57       ],
58       "metadata": {
59         "id": "xq4nPTAyTp_b"
60       }
61     },
62     {
63       "cell_type": "markdown",
64       "source": [
65         "### Rothermel formula"
66       ],
67       "metadata": {
68         "id": "txm9dcnmKDT8"
69       }
70     },
71     {
72       "cell_type": "markdown",
73       "source": [
74         "***Explain Rothermel's formula for fire rate of spread (ROS) here. You can write it in a form $R_0$ times 1+wind factor(wind speed)+slope factor(slope), without the details how are the wind factor and the slope factor computed. Include your code for Rothermel formula***"
75       ],
76       "metadata": {
77         "id": "no1eAxFiKHOq"
78       }
79     },
80     {
81       "cell_type": "markdown",
82       "source": [
83         "But the Rothermel formula is one dimensional - it assumes that the directions of the fire propagation, the wind, and the slope are the same. That is, that the three vectors are aligned. We will compare two approaches to extending the Rothermel formula to 2D fire propagation, in FARSITE and in WRF-SFIRE."
84       ],
85       "metadata": {
86         "id": "wfGV52UsM2Mq"
87       }
88     },
89     {
90       "cell_type": "markdown",
91       "source": [
92         "### Fire propagation by the ellipsoid method in FARSITE"
93       ],
94       "metadata": {
95         "id": "YhVxvWLTJm2q"
96       }
97     },
98     {
99       "cell_type": "markdown",
100       "metadata": {
101         "id": "E7kXfvt-Xn6P"
102       },
103       "source": [
104         "Richards (1990) and FARSITE (Finney, 2000) assume that fire spreads to an ellipsoid with axes $a$ and $b$, with the fire starting from a point at distance $c$ on the $b$-axis from the center of the ellipse. The $b$ axis is the direction of the maximal Rate of Spread (ROS), which equals to $b+c$, and is computed from the Rothermel formula. Richards (1990) considers only the wind and zero slope, then the direction of the maximal rate of spread is the wind direction. FARSITE computes a \"resultant vector\" from the slope and wind vectors, which it then substitutes into the Rothermel formula. To find and reproduce how are the computations of the slope and of the resultant vector done is the heart of the project.\n",
105         "\n",
106         "***Add formulas how are $a,b,c$ computed in the ellipsoid method using the Rothermel formula, from FARSITE manual and Richards (1990).. Add formulas what are the numbers substituted into the Rothermel formula and how they are computed from the wind vector and the slope vector. This includes computation of the \"resultant vector\" in FARSITE.***\n",
107         "\n",
108         "When the fire propagates from a fireline, the ellipsoid method considers it as starting from all points on the fireline, and the new fireline is then the envelope of the ellipsoids on the side in the propagation direction.\n",
109         "\n",
110         "***Add a picture of the envelope following Richards or FARSITE manual here. Note that their fireline is curved while the discussion here is for a straight fireline segment, you will need to draw your own for copyright reasons anyway***\n",
111         "\n",
112         "***Divide into subsections and code as appropriate***"
113       ]
114     },
115     {
116       "cell_type": "markdown",
117       "source": [
118         "### Fire propagation in WRF-SFIRE"
119       ],
120       "metadata": {
121         "id": "wQ4rp-EaJ11j"
122       }
123     },
124     {
125       "cell_type": "markdown",
126       "source": [
127         "WRF-SFIRE (Mandel et al., 2009, 2011) works with ROS in the direction of the normal to the fireline, and applies Rothermel's formula along the normal. That is, it substitutes in the Rothermel formula the wind speed projected on the normal (i.e., multiplied by the cosine of the wind vector and the normal vector), and the slope (i.e, slope of the gradient of the terrain height) also projected on the normal (i.e., multiplied by the cosine of the slope direction in the horizontal plane and the normal vector). WRF-SFIRE also includes modifications to impose a minimum lateral and backing fire spread."
128       ],
129       "metadata": {
130         "id": "ecTs44CcJ9Ug"
131       }
132     },
133     {
134       "cell_type": "markdown",
135       "metadata": {
136         "id": "hNwvmmloi5P5"
137       },
138       "source": [
139         "## Methods"
140       ]
141     },
142     {
143       "cell_type": "markdown",
144       "source": [
145         "To compare the fire propagation in WRF-SFIRE and FARSITE, we will find the ROS in the direction normal to the fireline that is equivalent to the propagation of the same fireline in the FARSITE ellipsoid method.\n",
146         "\n",
147         "<img src=\"http://math.ucdenver.edu/~jmandel/data/math4779f21/ellipsoid_ros2.png\" width=500  align=\"center\"/>"
148       ],
149       "metadata": {
150         "id": "UbND7AEmK5Un"
151       }
152     },
153     {
154       "cell_type": "markdown",
155       "source": [
156         "### Computing the rate of spread in the direction normal to the fireline from the fire propagation ellipsoid"
157       ],
158       "metadata": {
159         "id": "mmYmsag7Asoj"
160       }
161     },
162     {
163       "cell_type": "markdown",
164       "metadata": {
165         "id": "WkuzlJ2SMsi3"
166       },
167       "source": [
168         "Write the equation of an ellipse with horizontal axis $a$ and vertical axis\n",
169         "$b$ in parametric form\n",
170         "$$\n",
171         "\\left[\n",
172         "\\begin{array}\n",
173         "[c]{c}\n",
174         "x\\\\\n",
175         "y\n",
176         "\\end{array}\n",
177         "\\right]  =\\left[\n",
178         "\\begin{array}\n",
179         "[c]{c}\n",
180         "a\\cos s\\\\\n",
181         "b\\sin s\n",
182         "\\end{array}\n",
183         "\\right] \n",
184         "$$\n",
185         "with angle parameter $s$. Rotate by an angle $\\theta$,\n",
186         "$$\n",
187         "\\left[\n",
188         "\\begin{array}\n",
189         "[c]{c}\n",
190         "x\\\\\n",
191         "y\n",
192         "\\end{array}\n",
193         "\\right]  =\\left[\n",
194         "\\begin{array}\n",
195         "[c]{cc}\n",
196         "\\cos\\theta & \\sin\\theta\\\\\n",
197         "-\\sin\\theta & \\cos\\theta\n",
198         "\\end{array}\n",
199         "\\right]  \\left[\n",
200         "\\begin{array}\n",
201         "[c]{c}\n",
202         "a\\cos s\\\\\n",
203         "b\\sin s\n",
204         "\\end{array}\n",
205         "\\right]  ,\n",
206         "$$\n",
207         "and multiply out we get\n",
208         "$$\n",
209         "\\left[\n",
210         "\\begin{array}\n",
211         "[c]{c}\n",
212         "x\\\\\n",
213         "y\n",
214         "\\end{array}\n",
215         "\\right]  =\\left[\n",
216         "\\begin{array}\n",
217         "[c]{c}\n",
218         "a\\cos\\theta\\cos s+b\\sin\\theta\\sin s\\\\\n",
219         "-a\\sin\\theta\\cos s+b\\cos\\theta\\sin s\n",
220         "\\end{array}\n",
221         "\\right]  .\n",
222         "$$\n",
223         "Move the center vertically so that the point at distance $c$ from the center\n",
224         "along the $b$ axis is at $y=0$,\n",
225         "$$\n",
226         "\\left[\n",
227         "\\begin{array}\n",
228         "[c]{c}\n",
229         "x\\\\\n",
230         "y\n",
231         "\\end{array}\n",
232         "\\right]  =\\left[\n",
233         "\\begin{array}\n",
234         "[c]{c}\n",
235         "a\\cos\\theta\\cos s+b\\sin\\theta\\sin s\\\\\n",
236         "-a\\sin\\theta\\cos s+b\\cos\\theta\\sin s+c\\cos\\theta\n",
237         "\\end{array}\n",
238         "\\right]\n",
239         "$$\n",
240         "This is the equation of the ellipse from the figure. The rate of spread in the\n",
241         "direction of the normal equivalent to the ellipse is the distance of the\n",
242         "horizontal lines at $y=0$ and tangent to the top of the rotated shifted\n",
243         "ellipse\n",
244         "$$\n",
245         "R=\\max_{s}-a\\sin\\theta\\cos s+b\\cos\\theta\\sin s+c\\cos\\theta\n",
246         "$$\n",
247         "The find the highest point, set\n",
248         "$$\n",
249         "y^{\\prime}\\left(  s\\right)  =\\frac{\\partial}{\\partial s}\\left(  -a\\sin\n",
250         "\\theta\\cos s+b\\cos\\theta\\sin s+c\\cos\\theta\\right)  =0,\n",
251         "$$\n",
252         "which gives\n",
253         "$$\n",
254         "a\\sin\\theta\\sin s+b\\cos\\theta\\cos s=0\n",
255         "$$\n",
256         "We can divide by $\\sin\\theta\\neq0$,\n",
257         "$$\n",
258         "\\frac{\\sin s}{\\cos s}+\\frac{b}{a}\\frac{\\cos\\theta}{\\sin\\theta}=0,\n",
259         "$$\n",
260         "and compute $s$ from\n",
261         "$$\n",
262         "s=-\\arctan\\left(  \\frac{b\\cos\\theta}{a\\sin\\theta}\\right)\n",
263         "$$\n",
264         "Using the arctan2 function in numpy\n",
265         "$$\n",
266         "s=-\\text{arctan2}\\left(  b\\cos\\theta,a\\sin\\theta\\right)\n",
267         "$$\n",
268         "gives the correct result even for $\\sin\\theta=0.$ In any case, we get two solutions, $s$\n",
269         "and $s+\\pi$, plus an integer multiple of $2\\pi$,  substitute in the equation of the ellipse\n",
270         "$$\n",
271         "y=-a\\sin\\theta\\cos s+b\\cos\\theta\\sin s+c \\cos\\theta\n",
272         "$$\n",
273         "and take the larger value:\n",
274         "$$\n",
275         "R=\\max\\left\\{  u,-u\\right\\}  +c \\cos\\theta,\\quad u=-a\\sin\\theta\\cos\n",
276         "s+b\\cos\\theta\\sin s.\n",
277         "$$\n"
278       ]
279     },
280     {
281       "cell_type": "markdown",
282       "metadata": {
283         "id": "PzYQCUZ2i8PH"
284       },
285       "source": [
286         "### The code"
287       ]
288     },
289     {
290       "cell_type": "markdown",
291       "source": [
292         "The code to compute $R$ from $a,b,c,\\theta$ turns out to be just three lines."
293       ],
294       "metadata": {
295         "id": "UFYSjko3wlPI"
296       }
297     },
298     {
299       "cell_type": "markdown",
300       "source": [
301         ""
302       ],
303       "metadata": {
304         "id": "m95HJrgARw_F"
305       }
306     },
307     {
308       "cell_type": "code",
309       "metadata": {
310         "id": "MQM-prA63FJU"
311       },
312       "source": [
313         "import numpy as np\n",
314         "def ros_n(a,b,c,theta):\n",
315         "  # compute fire rate of spread in the direction normal to the fireline for fire\n",
316         "  # propagating according the the ellipsoid method with coefficients a, b, c \n",
317         "  # and the main axis of the ellipsoid at angle theta from the normal\n",
318         "  \n",
319         "  s = -np.arctan2(b*np.cos(theta),a*np.sin(theta))\n",
320         "  u = -a*np.sin(theta)*np.cos(s) + b*np.cos(theta)*np.sin(s)\n",
321         "  R = np.maximum(u,-u) + c*np.cos(theta)\n",
322         "  return R\n"
323       ],
324       "execution_count": null,
325       "outputs": []
326     },
327     {
328       "cell_type": "markdown",
329       "source": [
330         "## Results"
331       ],
332       "metadata": {
333         "id": "PW7r4-uFcEmH"
334       }
335     },
336     {
337       "cell_type": "markdown",
338       "source": [
339         "### Visualization"
340       ],
341       "metadata": {
342         "id": "PoO2k5EeBvSK"
343       }
344     },
345     {
346       "cell_type": "markdown",
347       "metadata": {
348         "id": "T7xRu4rPWI6k"
349       },
350       "source": [
351         "If it's not programmed and if it doesn't work it's just a fantasy. Let's draw some pictures to verify."
352       ]
353     },
354     {
355       "cell_type": "code",
356       "source": [
357         ""
358       ],
359       "metadata": {
360         "id": "s0OkBJzLcGfg"
361       },
362       "execution_count": null,
363       "outputs": []
364     },
365     {
366       "cell_type": "markdown",
367       "source": [
368         "#### Visualization code"
369       ],
370       "metadata": {
371         "id": "o1fgpn5gCWeo"
372       }
373     },
374     {
375       "cell_type": "code",
376       "metadata": {
377         "id": "ruy0KQ2M9DlD"
378       },
379       "source": [
380         "import matplotlib.pyplot as plt \n",
381         "def plot_ros(a,b,c,theta):\n",
382         "  r=ros_n(a,b,c,theta)\n",
383         "  def xe(s):   # x coordinate of point on the ellipse\n",
384         "    return a*np.cos(theta)*np.cos(s) + b*np.sin(theta)*np.sin(s)\n",
385         "  def ye(s):   # c coordinate of point on the ellipse\n",
386         "    return -a*np.sin(theta)*np.cos(s) + b*np.cos(theta)*np.sin(s) + c*np.cos(theta)\n",
387         "  def cline(t,m): # plot line through the center at angle t\n",
388         "    plt.plot([xe(t), xe(t+np.pi)], [ye(t), ye(t+np.pi)],marker='o',linestyle='-.',c=m)\n",
389         "  %matplotlib inline\n",
390         "  plt.figure(figsize=(8,8))\n",
391         "  s=np.linspace(0,2*np.pi,1000)  # parameter\n",
392         "  x = xe(s)\n",
393         "  y = ye(s)\n",
394         "  plt.plot(x,y,      linestyle='--',c='r',label='fire propagation ellipsoid at t=1s')\n",
395         "  cline(0.0,'b')\n",
396         "  cline(np.pi/2,'r')\n",
397         "  xx=np.linspace(-b,b,100)\n",
398         "  oo=np.ones(100)\n",
399         "  plt.plot(xx,oo*r,  linestyle='-',c='k',label='fireline at t=1s')\n",
400         "  plt.plot(xx,oo*0.0,linestyle='--',c='k',label='fireline at t=0s')\n",
401         "  plt.ylabel('fire traveled in normal direction (m)')\n",
402         "  plt.title('Normal ROS %s m/s for ellipsoid with a=%s m/s b=%s m/s c=%s m/s at %s rad angle' \n",
403         "            % (np.round(r,decimals=4),a,b,c,np.round(theta,decimals=4)))\n",
404         "  plt.axis('equal')\n",
405         "  plt.legend()\n",
406         "\n"
407       ],
408       "execution_count": null,
409       "outputs": []
410     },
411     {
412       "cell_type": "markdown",
413       "source": [
414         "#### Pictures"
415       ],
416       "metadata": {
417         "id": "LWyZhlDWCc5V"
418       }
419     },
420     {
421       "cell_type": "markdown",
422       "source": [
423         "No wind no slope:"
424       ],
425       "metadata": {
426         "id": "l_luyXeCOeWj"
427       }
428     },
429     {
430       "cell_type": "code",
431       "source": [
432         "plot_ros(1.0,1.0,0.0,0.0)"
433       ],
434       "metadata": {
435         "colab": {
436           "base_uri": "https://localhost:8080/",
437           "height": 499
438         },
439         "id": "CmWRz8-7OYLO",
440         "outputId": "6704d312-4f57-4657-ada2-67d733e466c6"
441       },
442       "execution_count": null,
443       "outputs": [
444         {
445           "output_type": "display_data",
446           "data": {
447             "image/png": "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\n",
448             "text/plain": [
449               "<Figure size 576x576 with 1 Axes>"
450             ]
451           },
452           "metadata": {
453             "needs_background": "light"
454           }
455         }
456       ]
457     },
458     {
459       "cell_type": "markdown",
460       "source": [
461         "##### Direction of the propagation of the fireline (the normal to the fireline) is the same as the maximum spread direction:"
462       ],
463       "metadata": {
464         "id": "GFBLs7l2B1_e"
465       }
466     },
467     {
468       "cell_type": "code",
469       "source": [
470         "plot_ros(2.0,4.0,1,0.0)"
471       ],
472       "metadata": {
473         "colab": {
474           "base_uri": "https://localhost:8080/",
475           "height": 499
476         },
477         "id": "_kFF8HI0BW7J",
478         "outputId": "a7b97194-cba6-4c4b-901d-a92252a040a8"
479       },
480       "execution_count": null,
481       "outputs": [
482         {
483           "output_type": "display_data",
484           "data": {
485 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\n",
486             "text/plain": [
487               "<Figure size 576x576 with 1 Axes>"
488             ]
489           },
490           "metadata": {
491             "needs_background": "light"
492           }
493         }
494       ]
495     },
496     {
497       "cell_type": "markdown",
498       "source": [
499         "When $\\theta=0$, the ROS in the ellipsoid method and the ROS in the normal direction as the same."
500       ],
501       "metadata": {
502         "id": "4C6Q-sfrDBDz"
503       }
504     },
505     {
506       "cell_type": "markdown",
507       "source": [
508         "##### The maximum ROS in the ellipsoid method at an angle to the normal direction:"
509       ],
510       "metadata": {
511         "id": "kXHX99-yDZPV"
512       }
513     },
514     {
515       "cell_type": "code",
516       "metadata": {
517         "id": "rFQwoV0V4xmG",
518         "colab": {
519           "base_uri": "https://localhost:8080/",
520           "height": 499
521         },
522         "outputId": "939ac3f8-0b91-4bbf-bf92-0e09a0e2c86f"
523       },
524       "source": [
525         "plot_ros(1.0,4.0,1,-1.0)"
526       ],
527       "execution_count": null,
528       "outputs": [
529         {
530           "output_type": "display_data",
531           "data": {
532 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\n",
533             "text/plain": [
534               "<Figure size 576x576 with 1 Axes>"
535             ]
536           },
537           "metadata": {
538             "needs_background": "light"
539           }
540         }
541       ]
542     },
543     {
544       "cell_type": "markdown",
545       "source": [
546         "Here, the ROS in the normal direction is *smaller* than the maximum ROS from the ellipsoid method."
547       ],
548       "metadata": {
549         "id": "AmRcCcjxDh6E"
550       }
551     },
552     {
553       "cell_type": "markdown",
554       "source": [
555         "##### The case when the the axes $a=b$ in the ellipsoid method and at angle to the fireline:"
556       ],
557       "metadata": {
558         "id": "BbunFGAvD1DV"
559       }
560     },
561     {
562       "cell_type": "code",
563       "metadata": {
564         "id": "teNrqbvoSL_i",
565         "colab": {
566           "base_uri": "https://localhost:8080/",
567           "height": 499
568         },
569         "outputId": "ea30e319-08db-4015-809e-ffd05f622a4d"
570       },
571       "source": [
572         "plot_ros(1.0,1.0,1.0,1.0)"
573       ],
574       "execution_count": null,
575       "outputs": [
576         {
577           "output_type": "display_data",
578           "data": {
579 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\n",
580             "text/plain": [
581               "<Figure size 576x576 with 1 Axes>"
582             ]
583           },
584           "metadata": {
585             "needs_background": "light"
586           }
587         }
588       ]
589     },
590     {
591       "cell_type": "markdown",
592       "source": [
593         "##### The case when the maximum ROS in the ellipsoid method is backwards to the propagation of the fireline"
594       ],
595       "metadata": {
596         "id": "0q_xMHguE_AI"
597       }
598     },
599     {
600       "cell_type": "code",
601       "metadata": {
602         "id": "hCuxGpWAEZEy",
603         "colab": {
604           "base_uri": "https://localhost:8080/",
605           "height": 499
606         },
607         "outputId": "0e90eae5-5153-423c-aae6-8046beaea5c2"
608       },
609       "source": [
610         "plot_ros(0.5,1.0,0.8,np.pi)"
611       ],
612       "execution_count": null,
613       "outputs": [
614         {
615           "output_type": "display_data",
616           "data": {
617             "image/png": "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\n",
618             "text/plain": [
619               "<Figure size 576x576 with 1 Axes>"
620             ]
621           },
622           "metadata": {
623             "needs_background": "light"
624           }
625         }
626       ]
627     },
628     {
629       "cell_type": "markdown",
630       "source": [
631         "So $b-c$ is the *backing ROS* - the speed with which fire propagates backwards."
632       ],
633       "metadata": {
634         "id": "VMysKTTOGCsv"
635       }
636     },
637     {
638       "cell_type": "markdown",
639       "source": [
640         "##### An example when the maximum ROS in the ellipsoid method points backwards at an angle:"
641       ],
642       "metadata": {
643         "id": "xz98N4taGSl3"
644       }
645     },
646     {
647       "cell_type": "code",
648       "metadata": {
649         "id": "W0DQBtLzFA37",
650         "colab": {
651           "base_uri": "https://localhost:8080/",
652           "height": 499
653         },
654         "outputId": "e3f489d5-1808-4c35-cdb2-855fa1b34258"
655       },
656       "source": [
657         "plot_ros(0.5,1.0,0.1,-2.0)"
658       ],
659       "execution_count": null,
660       "outputs": [
661         {
662           "output_type": "display_data",
663           "data": {
664 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\n",
665             "text/plain": [
666               "<Figure size 576x576 with 1 Axes>"
667             ]
668           },
669           "metadata": {
670             "needs_background": "light"
671           }
672         }
673       ]
674     },
675     {
676       "cell_type": "markdown",
677       "source": [
678         "##### The case when the maximum ROS in the ellipsoid method is aligned with the fireline:"
679       ],
680       "metadata": {
681         "id": "k7ruU2FyGz-9"
682       }
683     },
684     {
685       "cell_type": "code",
686       "source": [
687         "plot_ros(0.5,1.0,0.1,np.pi/2)"
688       ],
689       "metadata": {
690         "colab": {
691           "base_uri": "https://localhost:8080/",
692           "height": 499
693         },
694         "id": "oBBPDdqRHF10",
695         "outputId": "1b0ea4cf-c5ca-4cec-940b-437189142388"
696       },
697       "execution_count": null,
698       "outputs": [
699         {
700           "output_type": "display_data",
701           "data": {
702 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\n",
703             "text/plain": [
704               "<Figure size 576x576 with 1 Axes>"
705             ]
706           },
707           "metadata": {
708             "needs_background": "light"
709           }
710         }
711       ]
712     },
713     {
714       "cell_type": "markdown",
715       "source": [
716         "So $a$ becomes the *lateral ROS* - the speed how a fire propagates sidewise."
717       ],
718       "metadata": {
719         "id": "QwBbcA_YHUZe"
720       }
721     },
722     {
723       "cell_type": "markdown",
724       "source": [
725         "## Results"
726       ],
727       "metadata": {
728         "id": "JGu8uqdLVKHE"
729       }
730     },
731     {
732       "cell_type": "markdown",
733       "source": [
734         "***Add your comparison here. It would be based on a code that takes as input the fuels, wind vector $\\vec{w}$, slope vector $\\vec{s}$, and the normal vector to the fireline $\\vec{n}$ pointing in the direction of fire propagation. It would compute $a,b,c,\\theta$ for the FARSITE ellipsoid method. Then use the code above to compute the equivalent ROS in the normal direction, and compare with the ROS in the normal direction used in WRF-SFIRE.***\n",
735         "\n",
736         "***As discussed in class, the comparison can have some tables, and graphs where you keep everything constant except one quantity. For example,***\n",
737         "\n",
738         "***wind pointing in the normal direction, zero slope, vary wind speed (similar as in [WRF-SFIRE guide](https://wiki.openwfm.org/wiki/How_to_diagnose_fuel_properties_in_WRF-SFIRE#Diagnostics_provided)*** \n",
739         "\n",
740         "***constant wind and slope vectors, vary the normal direction (use polar plot) (particularly interesting)***\n",
741         "\n",
742         "***constant wind speed, zero slope, vary wind direction (use polar plot)***\n",
743         "\n",
744         "***constant wind speed, constant nonzero slope vector, vary wind direction (use polar plot)***\n",
745         "\n",
746         "***etc.***"
747       ],
748       "metadata": {
749         "id": "Nko_A39OVLuz"
750       }
751     }
752   ]