ATMS511_nonspherical_scatterers_tmatrix_CLASS.ipynb

{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"ATMS511_nonspherical_scatterers_tmatrix_CLASS.ipynb","version":"0.3.2","views":{},"default_view":{},"provenance":[],"collapsed_sections":[]},"kernelspec":{"name":"python2","display_name":"Python 2"}},"cells":[{"metadata":{"id":"tJPoGbOOhT2r","colab_type":"text"},"cell_type":"markdown","source":["# ATMS 511 Radation Lab: Scattering by non-spherical particles, a hands on investigation of T-matrix calculations using the pytmatrix module \n","\n","Today we will be investigating the pytmatrix package made by Jussi Leinonen at JPL, translated from FORTRAN (NASA GISS, http://www.giss.nasa.gov/staff/mmishchenko/t_matrix.html) to PYTHON. <br/>\n","\n","## Goals: \n","\n","The goals of this experiment are to <br/>\n","\n","1) Understand the effect of non-sphericity on the scattering parameters<br/>\n","2) Familiarize you with computational coding in python (in the cloud) <br/>"]},{"metadata":{"id":"jhm2cN2khax6","colab_type":"text"},"cell_type":"markdown","source":["## First thing first, lets install pytmatrix and miepython\n","\n","In this cloud version of python we need to install packages since every time you start is a fresh, clean version of python"]},{"metadata":{"id":"UNeKW8iBhjJX","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["!pip install pytmatrix\n","!pip install miepython"],"execution_count":0,"outputs":[]},{"metadata":{"id":"qWNQeG56jLHY","colab_type":"text"},"cell_type":"markdown","source":["## Great! \n","\n","Let's test the pytmatrix code"]},{"metadata":{"id":"uJp6lQGvhwSr","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["from pytmatrix.test import test_tmatrix\n","test_tmatrix.run_tests()"],"execution_count":0,"outputs":[]},{"metadata":{"id":"VIOuIP-glSu_","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["#T-matrix codes\n","from pytmatrix import tmatrix\n","from pytmatrix import scatter\n","import pytmatrix\n","#Mie codes \n","import miepython as mp\n","import numpy as np\n","#plotting package\n","%matplotlib inline\n","import matplotlib.pyplot as plt"],"execution_count":0,"outputs":[]},{"metadata":{"id":"36xDeoYjj0ei","colab_type":"text"},"cell_type":"markdown","source":["\n","\n","# Question 1: What is the difference between T-matrix and Mie theory?\n","\n","---\n","\n","\n"]},{"metadata":{"id":"oy6E5aR_kTjW","colab_type":"text"},"cell_type":"markdown","source":["## Please type the answer below:"]},{"metadata":{"id":"GmCL6aLckQO0","colab_type":"text"},"cell_type":"markdown","source":["Enter text here: Double click me\n"]},{"metadata":{"id":"pRTgYnrckEQD","colab_type":"text"},"cell_type":"markdown","source":["## What can pytmatrix supply us with?\n","\n","1) Asymetry parameter <br />\n","2) Phase function <br/>\n","3) Extinction Cross section <br/>\n","4) Scattering Cross section <br/>\n","5) Single Scatter Albedo <br/>\n","6) And microwave parameters (radar focused, thus backscatter focused) "]},{"metadata":{"id":"xSUa8jpcyZlT","colab_type":"text"},"cell_type":"markdown","source":["# Question 2: What is the scatter cross-section ($\\sigma_s$) in plain english? \n","\n","---\n","\n"]},{"metadata":{"id":"5aArc5nsymbb","colab_type":"text"},"cell_type":"markdown","source":["## Please type the answer below:"]},{"metadata":{"id":"7NugK3uSymbc","colab_type":"text"},"cell_type":"markdown","source":["Enter text here: Double click me\n"]},{"metadata":{"id":"E8UPyyvny6WT","colab_type":"text"},"cell_type":"markdown","source":["# Question 3: Plot the scatter cross-section of a aerosol particle and visable light with the following attributes using the t-matrix solution. \n","\n","---\n","\n","\n","\n","This first example will be given with many comments to help you learn how to use the package. After that we will formulate it on our own/together <br/>\n","\n","Assumptions: <br/>\n","1 spherical aerosol particle <br/>\n","m = 1.53 + 0.008i  <br/>\n","r = [0.01 to 1] microns <br/>\n","$\\lambda$ = 0.443 microns \n"]},{"metadata":{"id":"iyCrN2KbzFuI","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["#Step 1: code prescribed assumptions for the aerosol particle\n","r = np.linspace(0.01,1,20) #radii, microns\n","m = complex(1.53,0.008) #index of refraction \n","lambdaa = 0.443 #wavelength, microns\n","x = 2*np.pi*r/lambdaa #size parameter\n","\n","#Step 2: pre-allocate array to hold scatter objects\n","scat_obs = np.zeros(len(r),dtype=object)\n","\n","#Step 3: loop across radii\n","for i in np.arange(0,len(r)):\n","    #this is the format to create the scatter object. From the object we can calulate a whole list of scattering parameters\n","    t =  tmatrix.Scatterer(thet0=0,m=m,wavelength=lambdaa,radius=r[i],shape=tmatrix.Scatterer.SHAPE_SPHEROID,axis_ratio=1)\n","    #We will set the radius as the maximum radius to emulate the sphere\n","    t.radius_type = t.RADIUS_MAXIMUM\n","    #store object\n","    scat_obs[i] = t\n","\n","#Step 4: pre-allocate array to hold scatter cross-sections\n","sigma_s = np.zeros(len(r))\n","sigma_e = np.zeros(len(r))\n","#Step 5: loop across radii\n","for i in np.arange(0,len(r)):\n","    #to calculate all parameters we will use this syntax\n","    sigma_s[i] = pytmatrix.scatter.sca_xsect(scat_obs[i])\n","    sigma_e[i] = pytmatrix.scatter.ext_xsect(scat_obs[i])\n","\n","\n","#plot it up\n","fig =plt.figure(figsize=(10,5))\n","ax = plt.gca()\n","ax.plot(x,sigma_s,'-ob',markerfacecolor='w')\n","ax.set_xlabel('x',fontsize=16)\n","ax.set_ylabel(r'$\\sigma_{s}$, [$\\mu m^{2}$]',fontsize=16)\n","ax.grid('on')"],"execution_count":0,"outputs":[]},{"metadata":{"id":"Y9ek2z7g2yDM","colab_type":"text"},"cell_type":"markdown","source":["# Question 4: Compare the solution you got from T-matrix to the solution from the MIE code we used last week \n","\n","---\n","\n","\n","\n","Again here I will guide you through how to run miepython, but later on we will code it in real time"]},{"metadata":{"id":"LKAlckGp4tCd","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["#Note: all the varibles were set in running the code for pytmatrix. We will just reuse them with the exception of the refractive index, m \n","\n","#m in the mie code is defined as a m = (real - imaginary)\n","\n","m = complex(1.53,-0.008)\n","\n","#The mie code returns all of the efficiencies: \n","qext, qsca, qback, g = mp.mie(m,x)"],"execution_count":0,"outputs":[]},{"metadata":{"id":"dAiZOx2u7IH0","colab_type":"text"},"cell_type":"markdown","source":["## Q4a: What's the relationship between the efficiencies and the cross-sections?\n","\n","---\n","\n"]},{"metadata":{"id":"5E5pJxGL7Udl","colab_type":"text"},"cell_type":"markdown","source":["Enter text here: Double click me"]},{"metadata":{"id":"8ZRubYX0AYzQ","colab_type":"text"},"cell_type":"markdown","source":["## Q4b: What do you expect  to see when you plot both solutions?\n","\n","---\n","\n","\n"]},{"metadata":{"id":"k5soCaILAmTe","colab_type":"text"},"cell_type":"markdown","source":["Enter text here: Double click me"]},{"metadata":{"id":"nsITihD77UDD","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["### Fill in the equations here:\n","absorb  = \n","scatt   =\n","extinct = \n","###\n","\n","\n","###plot both\n","fig =plt.figure(figsize=(10,5))\n","\n","#simga_s is from t-matrix, scatt is from mie\n","\n","plt.plot(x,sigma_s,'-ob',markerfacecolor='w',lw=4,label='T-Matrix')\n","plt.plot(x,scatt,'--ow',markerfacecolor='w',lw=2,label='MIE')\n","\n","ax = plt.gca()\n","ax.legend(fontsize=16)\n","ax.set_xlabel('x',fontsize=16)\n","ax.set_ylabel(r'$\\sigma_{s}$, [$\\mu m^{2}$]',fontsize=16)\n","plt.show()\n","###"],"execution_count":0,"outputs":[]},{"metadata":{"id":"PKDkfKAbD6lU","colab_type":"text"},"cell_type":"markdown","source":["# Question 5: Plot all three (scattering, absorption and extinction) cross sections on one axis (using both mie and t-matrix).\n","\n","---\n","\n"]},{"metadata":{"id":"4iZ9ISEy8ZWx","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["\n","# Since we are re-running t-matrix, we need to set m back to positve imaginary comp.\n","m = complex(1.53,0.008)\n","\n","#loop across radii\n","for i in np.arange(0,len(r)):\n","    t =  tmatrix.Scatterer(thet0=0,m=m,wavelength=lambdaa,radius=r[i],shape=tmatrix.Scatterer.SHAPE_SPHEROID,axis_ratio=1)\n","    #We will set the radius as the maximum radius to emulate the sphere\n","    t.radius_type = t.RADIUS_MAXIMUM\n","    #store object\n","    scat_obs[i] = t\n","\n","#we already have sigma_s, but need sigma_a and sigma_e \n","sigma_a = np.zeros(len(r))\n","sigma_e = np.zeros(len(r))\n","#loop across radii\n","for i in np.arange(0,len(r)):\n","    #extinction cross section\n","    sigma_e[i] = pytmatrix.scatter.ext_xsect(scat_obs[i])\n","    #how do i get the absorption?\n","    sigma_a[i] = #Fill the right equation here\n","\n","    \n","###plot both\n","fig =plt.figure(figsize=(10,5))\n","plt.plot(x,sigma_s,'-ob',markerfacecolor='w',lw=4,label='Scatt_T')\n","plt.plot(x,sigma_a,'--ob',markerfacecolor='w',lw=4,label='Abs_T')\n","plt.plot(x,sigma_e,':ob',markerfacecolor='w',lw=4,label='Ext_T')\n","plt.plot(x,scatt,'-ow',markerfacecolor='w',lw=2,label='Scatt_M')\n","plt.plot(x,absorb,'--ow',markerfacecolor='w',lw=2,label='Abs_M')\n","plt.plot(x,extinct,':ow',markerfacecolor='w',lw=2,label='Ext_M')\n","ax = plt.gca()\n","ax.legend(fontsize=16)\n","ax.set_xlabel('x',fontsize=16)\n","ax.set_ylabel(r'$\\sigma$ [$\\mu m^{2}$]',fontsize=16)\n","plt.show()\n","###"],"execution_count":0,"outputs":[]},{"metadata":{"id":"06o9piU-uOwc","colab_type":"text"},"cell_type":"markdown","source":["# Question 6: Plot the mie and t-matrix solutions to the Q's"]},{"metadata":{"id":"6k113-1Yuk73","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["#Fill in the appro. equations here: \n","qext_t = \n","qsca_t = \n","qabs_t = \n","#\n","\n","\n","###plot both\n","fig =plt.figure(figsize=(10,5))\n","plt.plot(x,qsca_t,'-ob',markerfacecolor='w',lw=4,label='Scatt_T')\n","plt.plot(x,qabs_t,'--ob',markerfacecolor='w',lw=4,label='Abs_T')\n","plt.plot(x,qext_t,':ob',markerfacecolor='w',lw=4,label='Ext_T')\n","plt.plot(x,qsca,'-ow',markerfacecolor='w',lw=2,label='Scatt_M')\n","plt.plot(x,qext-qsca,'--ow',markerfacecolor='w',lw=2,label='Abs_M')\n","plt.plot(x,qext,':ow',markerfacecolor='w',lw=2,label='Ext_M')\n","ax = plt.gca()\n","ax.legend(fontsize=16)\n","ax.set_xlabel('x',fontsize=16)\n","ax.set_ylabel(r'Q',fontsize=16)\n","plt.show()\n","###"],"execution_count":0,"outputs":[]},{"metadata":{"id":"9Q3UBKoGKdxS","colab_type":"text"},"cell_type":"markdown","source":["Now that we proved that the code is the same for a sphere, lets exploit the benfit of t-matrix, non-sphericity (PS: We will not use the MIE code anymore)\n","\n","\n","# Question 7: Vary the axis-ratio and see how non-sphericity changes the scattering characteristics. Plot the cross-sections and Q's\n","\n","---\n","\n","Vary axis_ratio by changing the rotational axis. Use 0.8 and 0.6. <br/>\n"]},{"metadata":{"id":"3ceCpUynBVbS","colab_type":"text"},"cell_type":"markdown","source":["## Q7a: If we are changing the rotation axis to 0.8 and 0.6 what type of particle are we considering? (prolate/oblate)"]},{"metadata":{"id":"rxEmASd9Biwj","colab_type":"text"},"cell_type":"markdown","source":["Enter text here: Double click me"]},{"metadata":{"id":"N_DyvjAYMQCY","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["## Hint: To get started, look back to how we calculated the sphere. You can copy and paste\n","\n","#pre-allocate\n","scat_obs2 = np.zeros(len(r),dtype=object)\n","scat_obs3 = np.zeros(len(r),dtype=object)\n","#loop across radii\n","for i in np.arange(0,len(r)):\n","    ##Fill in the loop here: \n","    #\n","    #\n","    #\n","\n","#pre-allocate array to hold scatter cross-sections\n","sigma_s_8 = np.zeros(len(r))\n","sigma_a_8 = np.zeros(len(r))\n","sigma_e_8 = np.zeros(len(r))\n","\n","sigma_s_6 = np.zeros(len(r))\n","sigma_a_6 = np.zeros(len(r))\n","sigma_e_6 = np.zeros(len(r))\n","#loop across radii\n","for i in np.arange(0,len(r)):\n","    ##Fill in the loop here: \n","    #\n","    #\n","    #\n","    \n"],"execution_count":0,"outputs":[]},{"metadata":{"id":"-nEdewhxN58r","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["# Plot sigma here\n","\n","fig =plt.figure(figsize=(10,5))\n","\n","#sphere\n","plt.plot(x,sigma_s,'-ob',markerfacecolor='w',lw=4,label='Scatt_1.0')\n","plt.plot(x,sigma_a,'--ob',markerfacecolor='w',lw=4,label='Abs_1.0')\n","plt.plot(x,sigma_e,':ob',markerfacecolor='w',lw=4,label='Ext_1.0')\n","\n","#spheroid 1\n","plt.plot(x,sigma_s_8,'-or',markerfacecolor='w',lw=4,label='Scatt_0.8')\n","plt.plot(x,sigma_a_8,'--or',markerfacecolor='w',lw=4,label='Abs_0.8')\n","plt.plot(x,sigma_e_8,':or',markerfacecolor='w',lw=4,label='Ext_0.8')\n","\n","#spheroid 2\n","plt.plot(x,sigma_s_6,'-oy',markerfacecolor='w',lw=4,label='Scatt_0.6')\n","plt.plot(x,sigma_a_6,'--oy',markerfacecolor='w',lw=4,label='Abs_0.6')\n","plt.plot(x,sigma_e_6,':oy',markerfacecolor='w',lw=4,label='Ext_0.6')\n","\n","ax = plt.gca()\n","ax.legend(fontsize=16)\n","ax.set_xlabel('x',fontsize=16)\n","ax.set_ylabel(r'$\\sigma$, [$\\mu m^{2}$]',fontsize=16)\n","ax.set_title('Cross-Sections, oblate spheres',fontsize=16)\n","\n","plt.show()\n","\n","### "],"execution_count":0,"outputs":[]},{"metadata":{"id":"_0HxMQCeCYHE","colab_type":"text"},"cell_type":"markdown","source":["### Reminder: How do we calculate Q from $\\sigma$?"]},{"metadata":{"id":"1Ox7ki29v535","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["#Plot Q's here\n","\n"],"execution_count":0,"outputs":[]},{"metadata":{"id":"W225tBQAOruM","colab_type":"text"},"cell_type":"markdown","source":["## Q7b: Discuss the results in terms of what happens as this aerosol becomes more oblate (e.g. rotation axis --> 0.6)\n","\n","---\n","\n"]},{"metadata":{"id":"fAl6dQk9O6fV","colab_type":"text"},"cell_type":"markdown","source":["Enter text here: Double click me\n"]},{"metadata":{"id":"TbdfkKwiCmhC","colab_type":"text"},"cell_type":"markdown","source":["# Question 7 cont. : \n","\n","---\n","\n","Now change rotational axis to 1.2 and 1.4. What particle do we have now? (prolate vs oblate)"]},{"metadata":{"id":"luGGGLcO-qFp","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["## Hint: You can copy and paste\n","\n","#pre-allocate array to hold scatter cross-sections\n","scat_obs4 = np.zeros(len(r),dtype=object)\n","scat_obs5 = np.zeros(len(r),dtype=object)\n","#loop across radii\n","for i in np.arange(0,len(r)):\n","    ##Fill in the loop here: \n","    #\n","    #\n","    #\n","\n","#pre-allocate array to hold scatter cross-sections\n","sigma_s_12 = np.zeros(len(r))\n","sigma_a_12 = np.zeros(len(r))\n","sigma_e_12 = np.zeros(len(r))\n","\n","sigma_s_14 = np.zeros(len(r))\n","sigma_a_14 = np.zeros(len(r))\n","sigma_e_14 = np.zeros(len(r))\n","#loop across radii: \n","for i in np.arange(0,len(r)):\n","    ##Fill in the loop here: \n","    #\n","    #\n","    #\n","    \n","###"],"execution_count":0,"outputs":[]},{"metadata":{"id":"pG7gDcAVO0Jy","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["# Plot sigma here\n","\n","#sigmas\n","\n","fig =plt.figure(figsize=(10,5))\n","\n","#sphere \n","plt.plot(x,sigma_s,'-ob',markerfacecolor='w',lw=4,label='Scatt_1.0')\n","plt.plot(x,sigma_a,'--ob',markerfacecolor='w',lw=4,label='Abs_1.0')\n","plt.plot(x,sigma_e,':ob',markerfacecolor='w',lw=4,label='Ext_1.0')\n","\n","#spheroid 3\n","plt.plot(x,sigma_s_12,'-or',markerfacecolor='w',lw=4,label='Scatt_1.2')\n","plt.plot(x,sigma_a_12,'--or',markerfacecolor='w',lw=4,label='Abs_1.2')\n","plt.plot(x,sigma_e_12,':or',markerfacecolor='w',lw=4,label='Ext_1.2')\n","\n","#spheroid 4\n","plt.plot(x,sigma_s_14,'-oy',markerfacecolor='w',lw=4,label='Scatt_1.4')\n","plt.plot(x,sigma_a_14,'--oy',markerfacecolor='w',lw=4,label='Abs_1.4')\n","plt.plot(x,sigma_e_14,':oy',markerfacecolor='w',lw=4,label='Ext_1.4')\n","\n","ax = plt.gca()\n","ax.legend(fontsize=16)\n","ax.set_xlabel('x',fontsize=16)\n","ax.set_ylabel(r'$\\sigma$, [$\\mu m^{2}$]',fontsize=16)\n","ax.set_title('Cross-Sections, prolate spheres',fontsize=16)\n","plt.show()\n","\n","### "],"execution_count":0,"outputs":[]},{"metadata":{"id":"o4hRv9-hO7H7","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["#Plot Q's here\n","\n","\n","#"],"execution_count":0,"outputs":[]},{"metadata":{"id":"iL6CpnGLN5Di","colab_type":"text"},"cell_type":"markdown","source":["## Q7c: Discuss prolate spheroids against the sphere"]},{"metadata":{"id":"OFbifq8JOAEU","colab_type":"text"},"cell_type":"markdown","source":["Enter text here: Double click me"]},{"metadata":{"id":"AXoH4rZ8GKZh","colab_type":"text"},"cell_type":"markdown","source":["# Question 8: Compare a sphere against the cylinder"]},{"metadata":{"id":"pjTVfNaXs_2T","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["## Hint: You can copy and paste\n","\n","#pre-allocate\n","scat_obs6 = np.zeros(len(r),dtype=object)\n","#loop across radii\n","for i in np.arange(0,len(r)):\n","    ##Fill in the loop here: \n","    #\n","    #\n","    #\n","  \n","#pre-allocate array to hold scatter cross-sections\n","sigma_s_cyl = np.zeros(len(r))\n","sigma_a_cyl = np.zeros(len(r))\n","sigma_e_cyl = np.zeros(len(r))\n","\n","#loop across radii\n","for i in np.arange(0,len(r)):\n","    ##Fill in the loop here: \n","    #\n","    #\n","    #\n","    \n"],"execution_count":0,"outputs":[]},{"metadata":{"id":"-q6NWTA-GqNS","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["#sigmas\n","\n","fig =plt.figure(figsize=(10,5))\n","\n","plt.plot(x,sigma_s,'-ob',markerfacecolor='w',lw=4,label='Scatt_1.0')\n","plt.plot(x,sigma_a,'--ob',markerfacecolor='w',lw=4,label='Abs_1.0')\n","plt.plot(x,sigma_e,':ob',markerfacecolor='w',lw=4,label='Ext_1.0')\n","\n","plt.plot(x,sigma_s_cyl,'-or',markerfacecolor='w',lw=4,label='Scatt_cyl')\n","plt.plot(x,sigma_a_cyl,'--or',markerfacecolor='w',lw=4,label='Abs_cyl')\n","plt.plot(x,sigma_e_cyl,':or',markerfacecolor='w',lw=4,label='Ext_cyl')\n","\n","ax = plt.gca()\n","ax.legend(fontsize=16)\n","ax.set_xlabel('x',fontsize=16)\n","ax.set_ylabel(r'$\\sigma$, [$\\mu m^{2}$]',fontsize=16)\n","ax.set_title('Cross-Sections, sphere vs cylinder',fontsize=16)\n","plt.show()\n","\n","### "],"execution_count":0,"outputs":[]},{"metadata":{"id":"qmqI2l4DHGAa","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["#Plot Q's here\n","\n","\n","###"],"execution_count":0,"outputs":[]},{"metadata":{"id":"9rhFY1a5Jd1G","colab_type":"text"},"cell_type":"markdown","source":["## Write some obersvations between shapes:"]},{"metadata":{"id":"Sgs9O_TGJiQD","colab_type":"text"},"cell_type":"markdown","source":["Enter text here: Double click me"]},{"metadata":{"id":"CNd9VqI1JnH5","colab_type":"text"},"cell_type":"markdown","source":["# Question 9: Can you explain the relationship between the particle shape and the absorption efficiency? "]},{"metadata":{"id":"p4boAThPKyMK","colab_type":"text"},"cell_type":"markdown","source":["Enter text here: Double click me "]},{"metadata":{"id":"X-2Wh9tPNRCK","colab_type":"text"},"cell_type":"markdown","source":["# Question 10: Investigate the effect of non-sphericity on single scatter albedo.\n","\n","---\n","\n","Specifically: Use the a sphere, spheroid with axis_ratio = 1.0/0.8 and cylinder. <br/>\n","\n","Note: you already have the data needed to calculate this, no need to use the pytmatrix function"]},{"metadata":{"id":"jTAiM_XAH3ee","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["#SSA\n","\n","#What is the SSA again?\n","\n","### "],"execution_count":0,"outputs":[]},{"metadata":{"id":"KH0eQdE_aynr","colab_type":"text"},"cell_type":"markdown","source":["## Discuss:"]},{"metadata":{"id":"CmeG3KLDa1GN","colab_type":"text"},"cell_type":"markdown","source":["Enter text here: Double click me"]},{"metadata":{"id":"D-U-zpRxa4U8","colab_type":"text"},"cell_type":"markdown","source":["# Question 11: Investigate the effect of non-sphericity on the asymetry parameter\n","\n","---\n","\n","Specifically: Use the a sphere, spheroid with axis_ratio = 1.0/0.8, cylinder. <br/>\n","\n","Note: This one you will have to rerun the t-matrix\n","\n","### Q11a: What does the asymetry parameter tell us? "]},{"metadata":{"id":"FNUeyePzbUQ4","colab_type":"text"},"cell_type":"markdown","source":["Enter text here: Double click me"]},{"metadata":{"id":"y6T3hFtJIQZ-","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["#Step 2: pre-allocate array to hold scatter objects\n","scat_obs = np.zeros(len(r),dtype=object)\n","scat_obs2 = np.zeros(len(r),dtype=object)\n","scat_obs3 = np.zeros(len(r),dtype=object)\n","\n","#Step 3: loop across radii\n","for i in np.arange(0,len(r)):\n","    t =  tmatrix.Scatterer(thet0=0,m=m,wavelength=lambdaa,radius=r[i],shape=tmatrix.Scatterer.SHAPE_SPHEROID,axis_ratio=1)\n","    t.radius_type = t.RADIUS_MAXIMUM\n","    scat_obs[i] = t\n","    \n","\n","    t =  tmatrix.Scatterer(thet0=0,m=m,wavelength=lambdaa,radius=r[i],shape=tmatrix.Scatterer.SHAPE_SPHEROID,axis_ratio=1/0.8)\n","    t.radius_type = t.RADIUS_MAXIMUM\n","    scat_obs2[i] = t\n","    \n","    t =  tmatrix.Scatterer(thet0=0,m=m,wavelength=lambdaa,radius=r[i],shape=tmatrix.Scatterer.SHAPE_CYLINDER,axis_ratio=1)\n","    t.radius_type = t.RADIUS_MAXIMUM\n","    scat_obs3[i] = t\n","\n","#Step 4: pre-allocate array to hold scatter cross-sections\n","asym_sph = np.zeros(len(r))\n","asym_spo = np.zeros(len(r))\n","asym_cyl = np.zeros(len(r))\n","#Step 5: loop across radii\n","for i in np.arange(0,len(r)):\n","    #to calculate all parameters we will use this syntax\n","    asym_sph[i] = pytmatrix.scatter.asym(scat_obs[i])\n","    asym_spo[i] = pytmatrix.scatter.asym(scat_obs2[i])\n","    asym_cyl[i] = pytmatrix.scatter.asym(scat_obs3[i])"],"execution_count":0,"outputs":[]},{"metadata":{"id":"Q34ORBJjb_rg","colab_type":"code","colab":{"autoexec":{"startup":false,"wait_interval":0}}},"cell_type":"code","source":["#ASYM\n","\n","fig =plt.figure(figsize=(10,5))\n","\n","plt.plot(x,asym_sph,'-ob',markerfacecolor='w',lw=4,label='Sphere')\n","plt.plot(x,asym_spo,'-or',markerfacecolor='w',lw=4,label='Spheroid')\n","plt.plot(x,asym_cyl,'-oy',markerfacecolor='w',lw=4,label='Cylinder')\n","\n","ax = plt.gca()\n","ax.legend(fontsize=16)\n","ax.set_xlabel('x',fontsize=16)\n","ax.set_ylabel(r'Asymetry Param.,',fontsize=16)\n","ax.set_title('Asym., sphere vs spheroid vs cylinder',fontsize=16)\n","plt.show()\n","\n","### "],"execution_count":0,"outputs":[]},{"metadata":{"id":"wPHxzX0VdJDd","colab_type":"text"},"cell_type":"markdown","source":["## Discuss:"]},{"metadata":{"id":"o4OGkh89dJDf","colab_type":"text"},"cell_type":"markdown","source":["Enter text here: Double click me"]},{"metadata":{"id":"QtO8sXXndkT3","colab_type":"text"},"cell_type":"markdown","source":["# Concluding remarks:\n","\n","Looking over all the plots we made today what can we say we have learned?\n","\n","\n","\n"]},{"metadata":{"id":"u84Y8Vi3upq8","colab_type":"text"},"cell_type":"markdown","source":["Enter text here: Double click me"]},{"metadata":{"id":"LLpRSyPXdKIS","colab_type":"text"},"cell_type":"markdown","source":["# Congrats! \n","\n","This concludes Lab 1 of non-spherical scattering. Next class we will look into some databases of cataloged scattering of ice particles."]}]}