residual_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(ncdf4)\n",
    "library(viridis)\n",
    "library(fields)\n",
    "library(rstan)\n",
    "options(mc.cores = parallel::detectCores())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the working directory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "setwd('d:/dropbox/working/bayesian-matrixmodel/')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the data processing parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ndays            <- 4.0\n",
    "limit_to_numdays <- 4.0\n",
    "stride_t_obs     <- 10\n",
    "data             <- list()\n",
    "data$dt          <- 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Call the data processing script"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "source('data_processing.r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the `i_test` vector to partition test and training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data$i_test = c(rep(0,round(dim(data$obs)[2]*(2/3))),rep(1,round(dim(data$obs)[2]*(1/3))))\n",
    "print(names(data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compile, fit, and extract the free model that has a prior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mod_free    <- stan_model('d:/dropbox/working/bayesian-matrixmodel/stan_code/matrixmodel_freedelta_CV.stan')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mcmc_free    <- sampling(mod_free,    data=data, open_progress=TRUE,chains=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_free    <- extract(mcmc_free)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compile, fit, and extract the original allometric model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mod_orig    <- stan_model('d:/dropbox/working/bayesian-matrixmodel/stan_code/matrixmodel_orig_CV.stan')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mcmc_orig    <- sampling(mod_orig,    data=data, open_progress=TRUE,chains=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_orig    <- extract(mcmc_orig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compile, fit, and extract the sigmoidal model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mod_sig     <- stan_model('d:/dropbox/working/bayesian-matrixmodel/stan_code/matrixmodel_sigmoidaldelta_CV.stan')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mcmc_sig     <- sampling(mod_sig,     data=data, open_progress=TRUE,chains=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_sig     <- extract(mcmc_sig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compile, fit, and extract the free model without a prior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "mod_free_np <- stan_model('d:/dropbox/working/bayesian-matrixmodel/stan_code/matrixmodel_freedelta_no_prior_CV.stan')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "mcmc_free_np <- sampling(mod_free_np, data=data, open_progress=TRUE,chains=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_free_np <- extract(mcmc_free_np) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute mean predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "free_mean    <- apply(post_free$mod_obspos,c(2,3),mean)\n",
    "orig_mean    <- apply(post_orig$mod_obspos,c(2,3),mean)\n",
    "sig_mean     <- apply(post_sig$mod_obspos, c(2,3),mean)\n",
    "free_np_mean <- apply(post_free_np$mod_obspos,c(2,3),mean) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "free_resid    <- free_mean - data$obs\n",
    "orig_resid    <- orig_mean - data$obs\n",
    "sig_resid     <- sig_mean - data$obs\n",
    "free_np_resid <- free_np_mean - data$obs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate time variable with units of minutes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "xin <- seq(1,data$nt_obs*30,length.out=175)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the residual time series for each model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
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C13faNLDzRqlyxIDVdhxm/XN0byPo0g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\nAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width=7, repr.plot.height=4)\n",
    "par(mfrow=c(2,2),mar=c(3,4,2,3),oma=c(2,2,2,2))\n",
    "image.plot(x=xin,y=v,z=t(free_resid),xlab='',ylab=''); box(); mtext('free with prior')\n",
    "image.plot(x=xin,y=v,z=t(orig_resid),xlab='',ylab=''); box(); mtext('allometric')\n",
    "image.plot(x=xin,y=v,z=t(sig_resid),xlab='',ylab=''); box(); mtext('sigmoidal')\n",
    "image.plot(x=xin,y=v,t(free_np_resid),xlab='',ylab=''); box(); mtext('free no prior')\n",
    "\tmtext(side=1,outer=TRUE,'Time (minutes)')\n",
    "\tmtext(side=2,outer=TRUE,expression('Size ('*mu*'m)'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the size-specific model-data time series agreement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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D9lpL7cGK3c4V8h/T0K5geTiyThJPs2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\nM/8P66EDOBwBo20AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width=8, repr.plot.height=8)\n",
    "par(mfrow=c(5,3),mar=c(2,2,2,2),oma=c(2,3,2,2))\n",
    "for(i in 15:1) {\n",
    "\tplot(xin,data$obs[i,],ylim=c(0,0.25),cex=0.3,pch=3)    #plot the size-class time series\n",
    "\tlines(xin,sig_mean[i,],col='red',lwd=1.5)              #plot the sigmoidal fit\n",
    "    lines(xin,free_mean[i,],col='blue',lwd=1.5)            #plot the free with prior fit\n",
    "    lines(xin,orig_mean[i,],col='orange',lwd=1.5)          #plot the allometric fit\n",
    "    lines(xin,free_np_mean[i,],col='purple',lwd=1.5)\n",
    "\tmtext(round(v[i],3),cex=0.7)\n",
    "    if(i==15){legend('topleft',bty='n',legend=c('orig','free','free_np','sigmoid'),\n",
    "                    lty=1,\n",
    "                    col=c('orange','blue','purple','red'))}\n",
    "}\n",
    "mtext(side=1,outer=TRUE,'Time (minutes)',line=1)\n",
    "mtext(side=2,outer=TRUE,'Proportion of cells',line=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the autocorrelation function of the model errors per size class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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q8C0uWfdVmW14p/1Nx3Nec279u9Bkjn7yWYcKogyXU15zbv270CSLd/+vL/P3/1\nH89YuZ5Kvt0rgHS6/WPMQ7+PNEaup5Jv9wogXU/rsiBxvrg/lSijP6x53+4VQHq5HZGS/xpF\n2L2QG89YEUZ/XPO+3etdI6X/fSTX1Tyued/uNVbtXm+H79Q3zV1X87jmfbtXu48UXpNfkHVd\nzeOa9+1+yJMNrq84D2vet3s8IiQp1wvAvt2rLH+f7y9E8k0k11PJt3sVkG4kFUFyfaJ8OPO+\n3auA9OubJByR+oaPlmv3Ok82nK+P2XFAcv1942OY9+1e6RGhs/SP6M8h1/tk3+6VQLqSBJD6\nho+Wa/daIC2n8Jb55+GSB/MwtwgFy7QdN24ZuXZfNp+vTKwgl/9+ndLJy53WDmuCOHvmfbvv\nXm1uugtJ1YOYpSo1cebM+3ZvHqQhaWeJU0k6BUhqSWeJo6X7/lJf+3njLFU5xFTy7d6I+XqQ\n6j88etzhQTLl3iZIUpGzVOUQU8m3e4B02DiAJJ7UUBwj3cfLsny9hJc/smmPFKeSdBqQVJLO\nEkdP93m5NrrcRQoNJEGQK0VAOoff118Q+p380QYIgraKgPT9U1yVD61CkEslQHoNnwAJgsiK\nntr9/QynBad2EERWfLEhhPfLAemz/3ggaEpFl79Plyuk5SX5w3YQBG2FyyAIEhBAgiABASQI\nEhBAgiABaYDE/SZTuAeFRywhxbYlPe7WIbs/ovqY9+3eonkFkAIzb1gF3F4SUmxb0uPuHXL7\nI6qPed/uTZp/SvH2LpSSPrSNF6Y7a9Xsat63e2vmn1I8/v3Y1pScHD/mulTz2qyuP8qImJnq\nzft2b838DqSvQSDdzlu//06ryj6AUU1+fyT1Mu/bvUHzTyl+CfxoXv1uiXmcrtsthfv/Kvqj\njIiZqd68b/fWzD+l+Pc6CKTbi27VrOuPMiJmpnrzvt1bMx9JMeTU7vZCv5rrPcTcU8m3e2vm\nrYDEr0osgNj1/Cc3rt2bNC9Sv+ectXfldn8Qemm5K8eNo6iPed/uLZqP5vh9/j/5K75FAUFU\nxUA635Ya8AVZCCIqAtJHOF2+Gvt5Ch/dhwNBcyoC0kv4e/3z8pNcEARRlFu1w68IQRBR2SPS\nqfNgIGhWGb9GWq9N3l+vli2PfczMmL++HDKoripUwJJsr9qt75bdX2/uoFksqZQK5k1OJ1kV\nN78hxe8jvRq5j1SqpMGCyilvPhzb/FXTg2RGsUouz+8dVVnz4eDmryptfksyOKSVCpW0PfhW\nASSAJKVUJT0ckLLmw3J09xcVNr8pWRzTjxKVNLxjElTGvNULBWEVNr8pVQ2q6Xt/rI4e//xC\nalsAABV0SURBVNleZ6/e6S4L5nsNITKonl3nN78t1Ywq7F5oKVrJft3HZMX8GPt9a1+qgCXZ\nBunnLtzP65894sFBypv3AFKpApZkHCR7cm3eufucABJTrs07d59TrCDvL4VLyszHYW5RKpZu\nOnLkEnLtnmA+W5j9W+8tyefeUzWOfm7zvt0rgNT01Lfras5t3rd7BZDoB6L1Wuz2IDZpUTnD\nPpx53+4VQHoN/5rz+azm3OZ9u1cA6et0/tOaz+JKP0Gup5KU+zntq5zatS82+KwmQFq8bnqA\ntJHrqeTbvQJI5ZgMaIev5nHNi7mf0v4IkHJBx68mxbzIYLpLyv2U9lVAKv72d7pXB9UkmBcZ\nTHdJuZ/SvgZILb8i5LqaPyC5dj/ltlcAqel37QASQJpy2yuA1PTb366rCZAWr5s++4hQ0/K3\nx2oCpMXrps8fkSp++9t1NQHSclshbx9Mb9m9RpqwmABJIBwgPSSzajdhMQVB8ux+ym2vcx+p\n/re/ARJAmnLbD3myoZzPZzUB0uJ10wOkjQBSe/j3pp/OvzBIlwkg8/Q3QJpOAEkuHiAJhAMk\ngFSfZ8seGyQbha8cxc78nI9ISbnngWSkVFZAesrHBekY1fQJ0lP4DSRqMiunLpqPCJ3anmzg\nFMhIOQFSe3gNSAaKpQjSV+s1EuvwbmLmAaT2cB5ITOz0JAzSZ1ir7elvgDSZAJJg/Muao4pf\n5aoCqXqNUFqDQLJgfQFI0vFNrgDSHSS6eyvHL1mQSNkCq7WmLK/asS44DdQSIEmEA6Sd/rxW\n52OhcT+VHL94Mw6k4daXwSCNLoAGSG+Pq6TqfACJcTi2MI8u6g/SY8OPL4ACSD8cfVbn44D0\ngy2zmvLVB0jt4Rw0akFSqJYCSKfwezmHr69zSK3aZQ5YHUFSmH6MvWjWfAVIBkiSck9GY7Xh\nuXfvxcultGr3/v/R6G/qK7Jh92L3GedkrQ4klelH2Ylm2m5BIu9GJgKJuukrQCLveNiPzSyU\nxyeUQPq8/F5DarCiIIUNSHQ7lfUsJSX0m26rAZIYY+U0c4HEPoTlQxRAev3/1O4rvCx/LIMU\n+PUkNLcGUnJvwaaLUlxpkIp7rRqQ6jd8PkYBpM9Lf9cfQPlViBEAKTyBxL2yqKhnrgkhS6Zt\nBUjZeZQ0ydwjEy/bBoNE3fHkrtPiEZQhKYD0/wXS///5FcJbYWiExYbyXrAOpNBSz0wbep7y\nYgMTpPhhJ94bcS+1DiAMSXqxQQOkTU3IFV51kjyFpuTKddMYn8hHBSnUgbQuDL+exdHX6gkk\n6sRMtN6YDM+fsECiTVYp98TeuoC066R4vVKpsSA9zRVOOQMNjcew1p2kh03pPNfLbXTkmZGZ\nR9utLwWS4vV2M0jEenE2fKSTRN2EQQpb0YPDMVRXudGjlpJr9wzzhYJEitKcb7NksnuRSJFo\n/fMiFpNuHQl4apQePU/7g0rGya4CpX3tfrj74t7fzdYrkig6fKaiQ074jm/7dOvUls+3ziwt\n7FIaPbVbvxOfR5njcgVI2+7KJ9+Jz/RBug8xVgE+SMsu91Njyqp3cvhMxRcgdluwBaRICKv1\nLi4/eo6q4h+jpeTbG9zPh1QfnAPZegyZAa4aUUafGBjRfGoPeX8r3Trd8/6t6Mxk1Cs5/OQY\niJs+g0YpPRWNTGuCm8Lom+M/Xy/DeP0qxZCmYoqI8tDqwlpEWgZKty2AtPkkemqVBykGTGZm\nsieUtPufUQiBlIqIteZKA6Tz90jCKUESs5pRkEhjI5/ySkkVJEr/hersP4pBWquOICXz50BK\nRtBy56UA0kc4/7sM56PhyYbNW7UgLQtzHjZLfirx9pAV+1PB4qiAtDxt+MJw2SAt9NxZKYB0\nCv++x5MaFLeaEZDo42PPrBapgUTtv8KtXHF0QXr8Ld9BGqR0iMSJvwJI19O6HEjsK84GkPpK\n/nKbZ7fvbmPXO6UNb9M/QuiDiOGTXzbinubEs7QEx+Nfbkekln/V/OnN7hc7lWocWGIvwsg6\ntDoK7vl5K/a3IntnvWukpn9D9ulNgETNcESQmGke04QX1NqtQvzrbdI3/Buyu3c3IFXk7aPx\nU2lkdca7v6a5TxOZdORuNeI/m/8N2f37AMm8jLi/TROhbOReB8eT861AEu5SUEam0iBZcT9k\niiiA9Jr8Ql9dvtsHAMm6XLtXWv6WzPdIO+aYzZHrqeTbvdLyt2S++ycAybhcu1cA6d/rueLf\nc0nne3z0DVJ16g5yPZV8u1c5tXtIdjwAybZcu7cCEinE9ELDRZXDa9jxWJJr99Msf08h1/tk\n3+6nWf6eQq6nkm/38yx/zyDXU8m3+3mWv2eQ66nk2/1Ey98TyPVU8u3eyqqd1HjGyvVU8u0e\nIEnK9VTy7R7L35JyPZV8uwdIknI9lXy7VwHp9zn/xb7Mmd/xq3lY877da4B0vhUr9VXzsHsh\nN56xIoz+uOZ9u1cA6SOcPv//I/3jJ66reVzzvt2r3JD9e/0z+XNcrqt5XPO+3Ws+IiT1S6vz\nyPVU8u1e9Yh0SgV5vuI8rHnf7kdcI2mOZ6xcLwD7dj9i1U5zPGPleir5dq9zH4n4A5GuT5QP\nZ963ezzZICnX+2Tf7q2A5PqL+8cw79u9OEhfv65LDP9eKlYaBMYzVq73yb7dS4P0dQqvlz8/\nQ/KfkFUdz1i5nkq+3UuD9BJ+fX/R/M85+e+M5b6vFOYWoWCZtuPGLSPX7svm85XZ/vUzvD9e\nv4bUul2509phTRBnz7xv992rTUr3a/XDJ1/pG0nFQcxSlZo4c+Z9u7cJ0uYI13C4m6UqKuf1\nhwZJLekscbR0J4DULoB05Dhaul/h8/H683v9rmogs1RFJe7wIJlybxOkvz+L3l+n5GJDeSCz\nVOUQU8m3e5sgLW/h9H75FsXf91PhoVXX1TRl3rd7oyAt74+F9V+SaQ8Wp5J0GpBUks4SR073\n9Xb9DaH3mucaIMipVHZKEORNAAmCBASQIEhAAAmCBASQIEhAAAmCBASQIEhAAAmCBASQIEhA\nGiBxv7gb7kHhEUtIsW1Jj7t1yO6PqD7mfbu3aF4BpMDMG1YBt5eEFNuW9Lh7h9z+iOpj3rd7\nk+bHg7TxwnRnrZpdzft2b838eJBuh9tNrGo1r83q+qOMiJmp3rxv99bMmwHpdt76/XdaVfYB\njGry+yOpl3nf7g2aNwPS94sOu6Vw/19Ff5QRMTPVm/ft3pp5KyDdXnSrZl1/lBExM9Wb9+3e\nmnl3IK1/VnPuqeTbvTXzVkDiVyUWQOx6/pMb1+5NmlcAqf6u3O4PQi8td+W4cRT1Me/bvUXz\nGiBBkDsBJAgSEECCIAEBJAgSEECCIAEBJAgSkHGQ1muT67tpz58dUjnzy9HN593bm7jWxrPV\n+m7Zz+vVt1hsD79NOfM/dzKPqqz71QsrsjaeraLVXN+Ntj38NhXNH1o596sXZmRtPFvFd0ue\nQXLg+1s5948HfQzJ2ni2ylfz4JcJeZAObh4giQpHpJR5p9dI67M8W7I2nq0AklfzOfcmzVeN\nJ4T1VzsUZXEuuTZvwn2vIbBUM5ywe6Elg3PJtXkj7rsMgCnbID0WFMLq9djFBtfmrbjvMgCe\njINkT67NO3efE0BiyrV55+5zkl5sCHPLtXnf7gnms4VpjNfO11eNo5/bvG/3AElSrqeSb/dD\nQVoFPx0hJy0qZ9iHM+/bvdEjks9qzm3et3uAJCnXU0nK/Zz2rYLkspoAafG66QHSRq6nkpj7\nKe2PACm39j73XCKM+rjmxdxPaX/IESkTdPxqUsyLDKa7pNxPaX/MqV06ykE1CebnvEyScj/l\ntjd7jTRjMeWukVy7n3Lb2wXJYTUB0uJ10wOkjQBSe7jEE6ADBJAkJQeSZ/dTbnuAJCmA1B7O\nBcnITDEMkon68ASQ2sOZm/7a2kC1AJKkAFJ7eOChAZCy+QCSY/ccNG6tx1cLIEkKILWHAyQR\nras5vjpcAaT2cBZI4Q7S8HIBJEkBpPZw1jEGIBXyAaT5zA8AKQCkXZ7t4/W+QNqZn/M+mpT7\nKpBGl8sKSE/5fIH0FG5jZvA19Ig0ulymQRpdHLYAUns442QtrEFiPQ1RNUDVlFZAsjHvAFJ7\nuD5IKvvog4BkZOIBpPZwbZCCznUDQJKUKEgWDLHUGaTwBBL11hNAykQZmXgAqT1cGaRHa+Hy\nGgeJd4N7uEaBZMG7OEildFUg/bQWrtkhQGJip6dBINnYi3QGKexAovQPkLJBAMkCSROAtG4t\nO18AkqRkQeJdIrZ1LSGA1Ds+c2x9Bol4uGa01hRrtMlwG8tQfEm5D6RDcgSk8vrEE0iCNRsB\nUti92H1mE6TyXpKQI9P2+CBRN30ZpNANJGJqSirheCsgceferZNcC0KSTNsqkNgngrUqHyMI\nOTJt9UF6bk0qGjV3OZN4PAukcgeBV5hHR9zJR6BVGCTiDlPnxsi+n+LcJiTJtJUAqXQ2yAWJ\nkbuQqaTJQWKujJU6GQBSqAOpPDOeh1buRBykbGd8kPati0WjnwiaX2wI28BIh1UgVV6HFKov\nvNigDRJnN0I4xRFfbMj1JQUS67CXa5rLQ5D0+cQepFUPsa0ftiBRwai8DilUv7EaO5DW+RIz\nMJDmeCSKs9+hTVYp9y0gFQ5iPJA4rWcCKbr1W0FiXofkN7EiSIl5vN3W9J5YID1NqN2n2+HX\nShukWOs8G5zWQ0GKzJPJ5dq8b/cM84WCiCh68vy89wwhvYNYfZZ+se2x1DrqMboblNkn7/zs\nTmd/BhdtHXGSOtfntd73vzn5rPWdDE+PLZ0l6SQdQfW96eKpAvOAtH8nXp7ozMie6fJaP4eV\nRs9QCqR417FtnXRCBml/QpMYVOwsu0nxBYi4k1yauO9sx9EqlfowAFJIm4vv/SNXBi0gpYZT\nmHQEY5Q2TPNpvCJJYls4P0U2Hz0nynrYzTUF9wNBIvgYDVLuTIh8+Zs8WCSJ+HkRCUm2Jrsi\njl7A/LVpYnARl2SQ6L0v8TM+Qlim7TCQdidrBJBuhcuPnqNBIOUeTCiCFIlYNyKOID4qepM2\nkJLpIy7zU6RwAsvpm9FED6Rl37rsbj9PuJoVpPg+8fYB+2Rt1Yjcf7RrRhMdkKJnXfl9rYDv\neyJ6E7L7KEj5PgRAKhohjl43Xn0uPU+a8lUPaVdH6ZneRBek3ZvZqxMRjiyDVB7YjCDxr7eZ\n6XcdFK96SFuI0jOhja751EVg/UkLvWdKG657PkjLc2s+SAQjtNH3i9fIF9uvlLbC92ftPY8M\nv2eJnrsaAYkdHgOplKgCpIXXOhJfEyQYr5MvMmVKW6HXVYJieD61OkdK7vkgLTuQSN2zWu/D\nq6Lk4pXyReqhPo8WgKQR3gukx7UVa9A/0XVhYvFa+VJLc0Lp6b12DC8kV/c/OUi3U0LOkNfB\nlXFS8dr5NrmVMbINktQid6YDlfA9SJRUG5DaxkWTJ5D0ZRokdQGkgfHa+foKICmEV4C0bEBq\nGxZRAElSAEkhHCBZyNdXAEkh/AkkYjL60oSMAJKkAJJCeBVI6UcLlQSQJAWQNMKrQOpw32zb\n3eD4Rx5unUyq9mbeIcyruW8BqW5IFbICkla+vsIRSSN8AxIjH0CaVgBJJbwOpL71BEiSAkgq\n4bUg9RRAkhRAUglfgdTWhaIAkqQAkko4QBqfr68Akk44QBqer68Akk74A6S2HjQFkCQFkJTC\nAVI8KL0CY7hUBJEe8T+qeU33ACkbEwk2XCqCCKM/rnlN9y2/ptBHAElSAInahOu+2xf0agWQ\nJAWQqE347gFSOuZwcwkgUZsczj0WGySFxYZim6O6x/K3pLD8PS58sACSpFxPJd/uh4Lk+kT5\ncOZ9u8cRSVKu98m+3VsB6Rjftq4c/THM+3ZvBSStfH3lep/s2z1AkpTrqeTb/ZAbspmDeZhb\nrs37dl82n6+MTlDtsCaIs2fet/vu1ZZMV4yapSpNT0hJJm2J8+1+apDU0s4Sp5J0CpDUks4S\n1ydda9pZ4lSSAqQZ4sTTZSNnqYpK3OFBMuUeIB02DiCJJzUUJ57OdTVNmfftfnqQVNLOEqeS\ndBqQVJLOEtcnHQT5FECCIAEBJAgSEECCIAEBJAgSEECCIAEBJAgSEECCIAEBJAgSEECCIAEB\nJAgSkAZI3G/Ah3tQeMQSUmxb0uNuHbL7I6qPed/uLZpXACkw84ZVwO0lIcW2JT3u3iG3P6L6\nmPft3qT58SBtvDDdWatmV/O+3VszPx6k2+F2E6tazWuzuv4oI2Jmqjfv270182ZAup23fv+d\nVpV9AKOa/P5I6mXet3uD5s2A9P2iw24p3P9X0R9lRMxM9eZ9u7dm3gpItxfdqlnXH2VEzEz1\n5n27t2beHUjr36edeyr5dm/NvBWQ+FWJBRC7nv/kxrV7k+YVQKq/K7f7g9BLy105bhxFfcz7\ndm/RvAZIEOROAAmCBASQIEhAAAmCBASQIEhAAAmCBASQIEhAAAmCBASQIEhAAAmCBASQIEhA\nAAmCBASQIEhAAAmCBASQIEhAAAmCBASQeov8NbLPV0bwZzLNa/ojSE4AqbeoIH2Ff/Tgl3TS\nf+GL1iHUIoDUW1SQzm9CSd/OjERQpQBSbxFB+h07IFUl/Rd+MzJBdQJIvbWa85+vIZxuB563\nU3hbf/ZyvjV+D6f3/z8O4e0WHMLX6/W9+2/Qh/uPhy7Lx0s4fXznPodw/r48Or/ou3IvgNRb\nP7C8f//Q2pWk8+XVr5/P/oSP78bXRp/nW8NvkE6Xv71HQHq9vrgg+PGd+5rkI/zpadCnAFJv\n/cASLudcv69//wynv8vf089nb+Hvd5PzvwsU1/+e7iBd//ayAun26vPyyb9z+P9AdLrE/w7X\nY9HfwLncgqoEkHrr+XLmdii5nIV9/nx2/r5ECteDSbguvN2Bub+3B+n1GvQvvF7e+Fn1/hew\n3KAugNRba5C+Pt/Pt18pfPps88YWmGd81q/C/Wd5/7+mev37N9IlpCOUuLdWs/r8+DVqcZCW\n98uF1OnruUtISShxb/3M6l/h5ePzSxSkdUefby/f10gAqYNQ4t56guWrcI20/W8Enz/ra6Sn\nx4G+38Y1UgcBpN5ag/Rn+XtOrdr9+WmcAuklfFwW6cJ9OeL3JcvycVlsePleEbwekf5g1U5f\nAKm3NgsCV12QOf9c3Vz153KfqATS9WbR6zdSl8XxW5bLldHvn9TLO+4j6Qsg9dZqQeBXCOc/\nn+H6lPfb6f/XsScbljRIlxWFX9dXf16uIF2ebAi/risM1ycbvgHCkw0dBJAsaXUx8yn20PbX\n85UTpCCAZELXhxz+va4vZlhPf+eEp797CCCZ0O2xu9Pqrej3kSqE7yN10X+IHrQl5V4f5AAA\nAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width=7, repr.plot.height=6)\n",
    "par(mfrow=c(5,3),mar=c(2,2,1,2),oma=c(2,3,2,2))\n",
    "for(i in 15:1){\n",
    "\tacf(sig_resid[i,],lag.max=157,main='',ylim=c(-1,1),ci=0,xaxt='n')  #compute autocorrelation function\n",
    "\taxis(side=1,at=c(0,50,100,150),labels=c(0,50,100,150)*30)          #convert to minutes         \n",
    "\tmtext(round(v[i],3),cex=0.7)                                       #label with size class division\n",
    "}\n",
    "mtext(side=1,outer=TRUE,'Lag (minutes)',line=1)\n",
    "mtext(side=2,outer=TRUE,'Correlation of size-specific model errors',line=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the autocorrelation function of the total model error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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22Am7S850lZx9q65f19NnRPhtP6zklp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",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width=5, repr.plot.height=3)\n",
    "par(mar=c(4,4,2,2))\n",
    "acf(colSums(sig_resid),lag.max=157,main='',xaxt='n',xlab='',ylab='',ci=0,)\n",
    "    axis(side=1,at=c(0,50,100,150),labels=c(0,50,100,150)*30)               #convert to minutes\n",
    "    mtext(side=1,'Lag (minutes)',line=2.5)                \n",
    "    mtext(side=2,'Correlation of total model error',line=2.5)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the autocorrelation function of the model solution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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z4xShIgHW/pw4FAEgakXJr49MtHYK4eZv3IghQ/wyhQwQNSsdzVMDUEqVQUAqQp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\n9tCwAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "par(mfrow=c(5,3),mar=c(2,2,1,2),oma=c(2,3,2,2))\n",
    "for(i in 15:1){\n",
    "\tacf(sig_mean[i,],lag.max=157,main='',ylim=c(-1,1),ci=0,xaxt='n')  #compute autocorrelation function\n",
    "\taxis(side=1,at=c(0,50,100,150),labels=c(0,50,100,150)*30)         #convert to minutes\n",
    "\tmtext(round(v[i],3),cex=0.7)                                      #label with size class bin division\n",
    "}\n",
    "mtext(side=1,outer=TRUE,'Lag (minutes)',line=1)\n",
    "mtext(side=2,outer=TRUE,'Correlation of model size-specific model solution',line=1)"
   ]
  }
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