{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "38f854fa-0614-4a70-89fa-17acfc2ef9e9",
   "metadata": {},
   "source": [
    "# Data assimilation in MITgcm\n",
    "\n",
    "In this tutorial, we follow a modified MITgcm tutorial, `verification/lab_sea`, in which a regional spherical-polar coordinate ocean model is constrained to synthetic sea-surface temperature (SST) data via the adjoint method through automatic differentiation.\n",
    "\n",
    "## Goals\n",
    "1. Understanding MITgcm data assimilation workflows\n",
    "2. Gain physical intuition for what to expect when constraining a general circulation model to observational data, particularly with regards to model sensitivity to controls\n",
    "3. Probe model output using python tools `xmitgcm` and `xarray`\n",
    "\n",
    "```{tip}\n",
    "A Jupyter Notebook, [labsea_assim_tutorial](../../../assets/lab_sea/labsea_assim_tutorial) (after downloading, rename it to `labsea_assim_tutorial.ipynb`), is provided for users' convenience. It reproduces the steps and figures described in this visualization tutorial. Users can also add more sophisticated analysis on top of this notebook. `code` and `input` used to configure the MITgcm simulation can be found [here](https://github.com/ECCO-Hackweek/ecco-2024/blob/main/assets/lab_sea/).\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e72eeb4e-ed2c-48a3-baf2-5968c8885a2a",
   "metadata": {},
   "source": [
    "### The model\n",
    "We use a regional domain encompassing the Labrador Sea within the bounding box given by $79^\\circ $E, $41^\\circ $E,  $47^\\circ $N, and $77^\\circ $N. The domain has horizontal size $(n_x, n_y) = (16, 20)$ with $2^\\circ$ grid spacing in either horizontal direction. Unlike the verification exercises default configuration, we implement $n_z=21$ vertical levels. This tutorial takes advantage of the low number of spatial degrees of freedom combined with a short simulation time of 6 days to quickly demonstrate the key concepts to monitor when performing adjoint-based data assimilation. Higher resolution global ocean model adjoints are much more memory-intensive, but many of the same takeaways from this example will translate."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "796b910b-d2c3-4cce-9f5b-bcb5a7109f50",
   "metadata": {},
   "source": [
    "![alt text](labsea_bathy.png \"Labrador Sea Bathymetry\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "870e005d-51cd-4780-a845-14a37ff5bb75",
   "metadata": {},
   "source": [
    "### Run the forward model\n",
    "The regional model is initalized with bathymetry (pictured above), initial temperature $\\theta_0$, initial salinity $S_0$, external forcings, and a number of model parameters specified in files like [data](../../../assets/lab_sea/input/data) within the `input` directory. The model has been compiled with MITgcm `checkpoint68i` code with specific modifications made in `code`. The code directory is set up to compile the adjoint executable, but if one is just interested in simply analyzing model diagnostics or computing a misfit (but not *reducing* it), they can exclude `adjoint` from `code/packages.conf`. \n",
    "\n",
    "Let's examine some forward model output produces in the 0th run directory `run/iter0000`. We use `xmitgcm.open_mdsdataset` to load diagnostic and model grid data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "857f6cb4-1218-403f-894a-6cc4fa3ed387",
   "metadata": {},
   "source": [
    "### Load diagnostic data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "07b6d04a-81c6-4a2a-aa0d-059539c6f814",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import xarray as xr\n",
    "import xmitgcm\n",
    "from xmitgcm.utils import *\n",
    "import matplotlib.pyplot as plt\n",
    "import subprocess\n",
    "import glob\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "3713e233-54e4-4c6c-a824-3e2ca38e4be6",
   "metadata": {},
   "outputs": [],
   "source": [
    "root_dir = '/efs_ecco/mgoldber/MITgcm_c68i/verification/lab_sea/ecco_hackathon/'\n",
    "run_dir = root_dir + 'run/'\n",
    "run_dir0 = run_dir + 'iter0000/'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "0aa89eed-20bb-4de2-bf5d-4c6beb5de5f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "prefix = 'diags3d' # other available daily diagnostics found in this run:\n",
    "                   # diags2D, diagsEXF, diagsSI, diagsKPP\n",
    "\n",
    "ds = xmitgcm.open_mdsdataset(run_dir0,\n",
    "                        grid_dir = run_dir0,\n",
    "                        prefix = [prefix],\n",
    "                        default_dtype=np.float32,\n",
    "                        delta_t=900,\n",
    "                        ref_date='1979-01-01 00:00:00'\n",
    "                            )\n",
    "ds['XC'] = xr.where(ds.XC > 180, ds.XC - 360, ds.XC)\n",
    "ds['XG'] = xr.where(ds.XG > 180, ds.XG - 360, ds.XG)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f251fb8d-69cb-480b-a676-d48d171c0291",
   "metadata": {},
   "source": [
    "### Look at model-data misfit\n",
    "The observational data used in this experiment is comprised of a single SST field occuring in the sixth record of the file `labsea_SST_fields_linear_rec006`. Our specifications in `data.ecco` instruct the model to compute a misfit between the model SST and this dataset on the sixth day of the run. Let's add the dataset to our dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "379850d9-6b4a-4883-90b3-444a0ae20c47",
   "metadata": {},
   "outputs": [],
   "source": [
    "nz, nx, ny = ds.hFacC.shape\n",
    "nday = 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "1e4a1568-4bdc-4c5e-b15a-7225da0c7e2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_sst = read_raw_data(run_dir0 + '/labsea_SST_fields_linear_rec006', dtype=np.dtype('>f8'), shape=(nday, nx, ny))\n",
    "data_sst[data_sst==-9999] = np.nan\n",
    "ds['data_sst'] = xr.DataArray(data_sst, dims=['time','YC','XC'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "370a19a8-b875-4a1b-a26a-3d3527dc0896",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1200x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vmin, vmax = (-12, 12)\n",
    "cmap = plt.get_cmap('RdBu_r')\n",
    "cmap.set_bad(color='#d3d3d3')\n",
    "\n",
    "def plot_model_data_misfit(ds):\n",
    "    \n",
    "    fig, axes = plt.subplots(1, 3)\n",
    "    (ax1, ax2, ax3) = axes\n",
    "\n",
    "    model_sst = ds.THETA.isel(time=5, Z=0).where(ds.hFacC.isel(Z=0))\n",
    "    p = model_sst.plot(ax=ax1, cmap=cmap, vmin=vmin, vmax=vmax, extend='both', add_colorbar=False)\n",
    "    ax1.set_title('Model SST', fontsize=20)\n",
    "    ax1.set_ylabel('Latitude', fontsize=14)\n",
    "    ax1.set_xlabel('Longitude', fontsize=14)\n",
    "    \n",
    "    \n",
    "    data_sst = ds.data_sst.isel(time=5).where(ds.hFacC.isel(Z=0))\n",
    "    p = data_sst.plot(ax=ax2, vmin=vmin, vmax=vmax, cmap=cmap, extend='both', add_colorbar=False)\n",
    "    ax2.set_title('Data SST', fontsize=20)\n",
    "    ax2.set_ylabel('')\n",
    "    ax2.set_xlabel('Longitude', fontsize=14)\n",
    "    \n",
    "    misfit_sst_offline = (model_sst - data_sst)\n",
    "    p = misfit_sst_offline.plot(ax=ax3, vmin=vmin, vmax=vmax, cmap=cmap, extend='both', add_colorbar=False)\n",
    "    ax3.set_title('Model - Data', fontsize=20)\n",
    "    ax3.set_xlabel('Longitude', fontsize=14)\n",
    "    ax3.set_ylabel('')\n",
    "    \n",
    "    cbar_ax = fig.add_axes([0.1, -0.05, 0.8, 0.05])  # Position [left, bottom, width, height]\n",
    "    cbar = fig.colorbar(p, cax=cbar_ax, orientation='horizontal')\n",
    "    cbar_ax.tick_params(labelsize=16)\n",
    "    cbar.ax.set_xlabel('Potential Temperature [degC]', fontsize=14)\n",
    "    \n",
    "    ax1.tick_params(axis='both', labelsize=13)\n",
    "    ax2.tick_params(axis='both', labelsize=13)\n",
    "    ax3.tick_params(axis='both', labelsize=13)\n",
    "    \n",
    "    fig.set_size_inches(12,4)\n",
    "    fig.tight_layout()\n",
    "    return fig, axes\n",
    "fig, axes = plot_model_data_misfit(ds)\n",
    "#fig.savefig('model_data_misfit_spatial.png', dpi=500, bbox_inches='tight', facecolor='white')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44892433-1e56-4f25-9daf-bfe8bbfa4e68",
   "metadata": {},
   "source": [
    "### Compute model-data misfit by hand\n",
    "By the end of a forward run compiled with `pkg/ecco` and `pkg/cost`, a file `costfunctionXXXX` is created containing the scalar cost functional $J:\\mathbb{R}^n\\rightarrow\\mathbb{R}$ given by\n",
    "$\n",
    "J({\\bf u}) = \\frac{1}{2}\\left({\\bf d} - \\textbf{Obs}({\\bf u})\\right)^T{\\bf R}^{-1}\\left({\\bf d} - \\textbf{Obs}({\\bf u})\\right) \n",
    "+\\frac{1}{2}({\\bf u} - {\\bf u}_0)^T{\\bf B}^{-1}({\\bf u} - {\\bf u}_0).\n",
    "$\n",
    "In the first term, the misfit captures the discrepency between model and data, weighted by the our uncertainty in the observations. The second term acts as a numerical regularizer for the ill-posed inverse problem, penalizing deviations from the initial guess ${\\bf u}_0$. The table below describes the terms of $J$, with notation taken from [Loose & Heimbach (2021)](https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2020MS002386).\n",
    "| Variable                       | Description                                                                                                          |\n",
    "|--------------------------------|----------------------------------------------------------------------------------------------------------------------|\n",
    "| $ J({\\bf u}) $                | cost function, i.e. the scalar misfit between the model and observations                              |\n",
    "| $ {\\bf d} $                   | observational data vector                         |\n",
    "| $ \\textbf{Obs}({\\bf u}) $     | observation operator giving the \"model equivalent\" to the data                                   |\n",
    "| $ {\\bf R} $                   | observational data error covariance matrix, representing the uncertainties in the observations $ {\\bf d} $       |\n",
    "| $ {\\bf u} $                   | control variables, such as initial conditions, boundary conditions (e.g. atmospheric forcing or regional open boundaries), or model parameters |\n",
    "| $ {\\bf u}_0 $                 | prior estimate of the control variables, serving as a reference or initial guess                               |\n",
    "| $ {\\bf B} $                   | background error covariance matrix, representing uncertainties in the prior estimate $ {\\bf u_0} $          |\n",
    "\n",
    "We aim to constrain our model trajectory towards the data, thereby reducing the cost. Let's compute the misfit offline to confirm we have a full understanding of how the model is coming up with $J$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "3e3e2901-d8e2-4425-b06c-5ca56c0af81c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "online:  J_SST = 2.122397e+07\n",
      "offline: J_SST = 2.122426e+07\n",
      "relative error = 0.001353%\n"
     ]
    }
   ],
   "source": [
    "## ONLINE\n",
    "# grep the cost directly from costfunctionXXXX file\n",
    "def grep_cost(run_dir, field_name='fc', ioptim=0):\n",
    "    costfunction_filename = f'{run_dir}/costfunction{ioptim:04d}'    \n",
    "    sysstr='grep ^{}.* {} | awk \\'{{print $3}}\\' |  sed \\'s/D/E/g\\''\\\n",
    "            .format(field_name, costfunction_filename)\n",
    "    grepstr = subprocess.check_output(sysstr, shell=True)\n",
    "    grepfloat = float(grepstr.decode().strip('\\n'))\n",
    "    return grepfloat\n",
    "J_online = grep_cost(run_dir0, ioptim=0)\n",
    "\n",
    "## OFFLINE\n",
    "# SST weight: spatially uniform, values of 1.042 deg C\n",
    "model_sst_day6 = ds.THETA.isel(time=5, Z=0).where(ds.hFacC.isel(Z=0))\n",
    "data_sst_day6 = ds.data_sst.isel(time=5).where(ds.hFacC.isel(Z=0))\n",
    "\n",
    "misfit_sst_weight = read_raw_data(run_dir0 + 'sigma_sst_p010402.bin', dtype=np.dtype('>f8'), shape=(nx, ny))\n",
    "J_offline = (((model_sst_day6 - data_sst_day6) / misfit_sst_weight)**2).sum().values\n",
    "\n",
    "print(\n",
    "      f'online:  J_SST = {J_online:0.6e}\\n'\\\n",
    "      f'offline: J_SST = {J_offline:0.6e}\\n'\n",
    "      f'relative error = {100 * abs(J_offline - J_online)/abs(J_online):f}%'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b46da5e-7797-4d33-8c1c-64ad51d2cf8a",
   "metadata": {},
   "source": [
    "### Run the adjoint code, look at gradients $\\partial J/\\partial\\text{xx}$\n",
    "We now run the adjoint model and produce *gradients* or *sensitivities*. Here, we compute gradients of $J$ with respect to controls ${\\bf u}$. The MITgcm also gives users the ability to look at sensitivites of a number of diagnostics to said controls, but here we will restrict our focus to the cost.\n",
    "\n",
    "In this run, we control the 3d initial temperature field, $\\theta_0$, and the 2d time-varying air temperature, $\\text{atemp}$. Let's form a hypothesis for what the gradients will look like: \n",
    "- $\\partial J/\\partial \\theta_0$: Recall we found that the data was warmer than the model giving rise to a negative misfit. As such, we expect that an increase in the initial temperature $\\theta_0$ should decrease the cost $J$, thus $\\partial J/\\partial T_0 < 0$.\n",
    "- $\\partial J/\\partial \\text{atemp}$: Similarly, an increase in air temperature raises sea surface temperature. Therefore we expect the same relationship for $\\partial J/\\partial \\text{atemp}$, that an increase in $\\text{atemp}$ will decrease the cost $J$, or $\\partial J/\\partial T_0 < 0$.\n",
    "\n",
    "In this simple setup, we will see that we can confirm our hypotheses. In more complicated models, however, deeper knowledge of the model dynamics is critical towards understanding the more complex sensitivities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b2557788-e058-4e53-ad8f-970d659532b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# load dJ/dtheta\n",
    "ioptim = 0\n",
    "adxx_theta = read_raw_data(run_dir0 + f'adxx_theta.{ioptim:010d}.data', dtype=np.dtype('>f8'), shape=(nz, nx, ny))\n",
    "ds['adxx_theta'] = xr.DataArray(adxx_theta,\n",
    "                                dims=ds['THETA'].isel(time=0).dims,\n",
    "                                coords=ds['THETA'].isel(time=0).coords)\n",
    "# plot dJ/dtheta\n",
    "vmax = np.nanmax(abs(adxx_theta))\n",
    "vmin = -vmax\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "p = ds.adxx_theta.where(ds.hFacC[0]).isel(Z=0).plot(\\\n",
    "                                         x=\"XC\",y=\"YC\",\n",
    "                                         cmap=cmap, vmin=vmin, vmax=vmax, add_colorbar=False)\n",
    "cbar = fig.colorbar(p, ax=ax)\n",
    "cbar.ax.tick_params(labelsize=12)\n",
    "cbar.ax.set_ylabel('[dJ/degC]', fontsize=14)\n",
    "ax.set_ylabel('Latitude', fontsize=14)\n",
    "ax.set_xlabel('Longitude', fontsize=14)\n",
    "\n",
    "ax.set_title(r'$\\frac{\\partial J}{\\partial {\\mathrm{SST}_0}}$', fontsize=30, pad = 20)\n",
    "ax.tick_params(axis='both', labelsize=14)\n",
    "\n",
    "fig.set_size_inches(6,5)\n",
    "fig.tight_layout()\n",
    "#fig.savefig('dJdSST.png', dpi=500, bbox_inches='tight', facecolor='white')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21dcbcb8-8061-4d98-bf15-407621d0f571",
   "metadata": {},
   "source": [
    "We can do the same for the 2D time-varying control $\\mathrm{atemp}$. Below, we plot snapshots of the gradients at different time lags propagating backwards in time through the adjoint run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "537e2b6a-a0cd-4cfe-a2bd-da6203edda04",
   "metadata": {},
   "outputs": [],
   "source": [
    "nrec = nday + 1 # using knowledge of the number of records in this file \n",
    "                # read_mds would be preferable here, but I don't think it\n",
    "                # properly implements nrec\n",
    "\n",
    "adxx_atemp = read_raw_data(run_dir0 + f'adxx_atemp.{ioptim:010d}.data', dtype=np.dtype('>f8'), shape=(nrec, nx, ny))\n",
    "adxx_atemp[adxx_atemp == 0.] = np.nan\n",
    "\n",
    "fig, axes = plt.subplots(2, 3)\n",
    "\n",
    "set_cbar = True\n",
    "\n",
    "for i, ax in enumerate(axes.ravel()):\n",
    "    fld = adxx_atemp[::-1][i]  # time-reversed order, how the adjoint operates\n",
    "\n",
    "    vmax = 1e3 if set_cbar else np.nanmax(abs(fld))\n",
    "    vmin = -vmax\n",
    "\n",
    "    # Add the field to the dataset for convenient lat/lon axis ticks on 2D plots\n",
    "    ds['fld'] = xr.DataArray(fld, dims=ds['rA'].dims, coords=ds['rA'].coords)\n",
    "    p = ds.fld.where(ds.hFacC[0]).plot(ax=ax, vmin=vmin, vmax=vmax, cmap=cmap, add_colorbar=False)\n",
    "\n",
    "    ax.set_title(r'$\\frac{\\partial J}{\\partial {\\mathrm{atemp}}}$' + f' (lag {i} day)', fontsize=16)\n",
    "\n",
    "    ax.set_xlabel('Longitude' if i >= 3 else '', fontsize=14)\n",
    "    ax.set_ylabel('Latitude' if i % 3 == 0 else '', fontsize=14)\n",
    "    \n",
    "cbar_ax = fig.add_axes([0.1, -0.05, 0.8, 0.03])  # Position [left, bottom, width, height]\n",
    "cbar = fig.colorbar(p, cax=cbar_ax, orientation='horizontal')\n",
    "cbar_ax.tick_params(labelsize=16)\n",
    "cbar.ax.set_xlabel('Sensitivity to air temperature [dJ/degK]', fontsize=14)\n",
    "\n",
    "fig.set_size_inches(10, 7)\n",
    "fig.tight_layout()\n",
    "\n",
    "#fig.savefig('dJdatemp.png', dpi=500, bbox_inches='tight', facecolor='white') # Vectorized PDF\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9d783d2-ba6b-49a9-8c23-b7164f584b4c",
   "metadata": {},
   "source": [
    "As expected, the sensitivities are all negative. We can use the gradients to minimize our cost function through gradient descent.\n",
    "\n",
    "$\\mathbf{u}^{(k)} - \\alpha \\nabla J(\\mathbf{u}^{(k)})=:\\mathbf{u}^{(k+1)}$\n",
    "\n",
    "Any number of optimization libraries facilitate this step. We proceed using the library [optim_m1qn3](https://github.com/mjlosch/optim_m1qn3), which implements a limited memory quasi-Newton (L-BFGS) algorithm. Specifying the `doMainPack` option inside `data.ctrl`, we bundle up our gradient information into a binary file `ecco_ctrl_MIT_CE_000.opt0000`, hand it off to `optim_m1qn3`, and run the optimization, obtaining a ${\\bf u}^{(k+1)}$ in the file `ecco_ctrl_MIT_CE_000.opt0001`, which we refer to as the first iteration *control adjustment*. When we run our model with these perturbed controls, we will find that the cost $J$ decreases.\n",
    "\n",
    "There are various options available to the user when performing the optimization step specified in `data.optim` (see warning below). Of note, the user must indicate a desired cost reduction through e.g. the parameter `dfminFrac`. Typically, reductions of 2%-5% are attainable. Later on, we will plot the cost function reduction across 10 optimization iterations to see how well we did.\n",
    "\n",
    "> :::{warning}\n",
    "> Confusingly, `data.optim` is also an input file used by MITgcm to instruct the model what optimization iteration it is running, but this is different from the file named `data.optim` used by `optim_m1qn3`. Furthermore, both softwares use input files by the name of `data.ctrl`, but they serve completely different purposes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "affe3ea9-0b47-496a-a18b-a0abf460e032",
   "metadata": {},
   "source": [
    "### Examine control adjustments\n",
    "Below we load the adjustment made to the initial temperature control $\\theta_0$. We plot the top level of the 3D array, the initial SST adjustment. Additionally, we confirm our understanding that \n",
    "$$\\theta_0^0 + \\delta\\theta_0^1 =: \\theta_0^1$$\n",
    "where the subscripts denote initial temperature and the superscripts denote optimization iteration. Unsurprisingly, the perturbation is all positive. This makes sense knowing that the model was initially cooler than the data. In other words, the new initial condition we use for the next run is a perturbed (*warmer*, specifically) value of the old initial condition that will lead the model SST to be more similar to the data on day 6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "43ad4be4-b720-400f-bbc3-2efcb5e5d1e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "run_dir0 = f'{run_dir}/iter{0:04d}/'\n",
    "run_dir1 = f'{run_dir}/iter{1:04d}/'\n",
    "\n",
    "# load control adjustments\n",
    "xx_theta = read_raw_data(run_dir1 + f'xx_theta.{1:010d}.data', dtype=np.dtype('>f8'), shape=(nz, nx, ny))\n",
    "xx_atemp = read_raw_data(run_dir1 + f'xx_atemp.{1:010d}.data', dtype=np.dtype('>f8'), shape=(nrec, nx, ny))\n",
    "xx_theta[xx_theta == 0.] = np.nan\n",
    "xx_atemp[xx_atemp == 0.] = np.nan\n",
    "\n",
    "# load initial theta\n",
    "theta0_iter0 = read_raw_data(run_dir0 + f'T.{0:010d}.data', dtype=np.dtype('>f4'), shape=(nz, nx, ny))\n",
    "theta0_iter0[theta0_iter0==0.] = np.nan\n",
    "theta0_iter1 = read_raw_data(run_dir1 + f'T.{0:010d}.data', dtype=np.dtype('>f4'), shape=(nz, nx, ny))\n",
    "theta0_iter1[theta0_iter1==0.] = np.nan\n",
    "\n",
    "# slice out SST\n",
    "SST0_iter0 = theta0_iter0[0, :, :]\n",
    "SST0_iter1 = theta0_iter1[0, :, :]\n",
    "\n",
    "# confirm that \\theta_0 + \\delta\\theta = \\theta_1\n",
    "assert np.allclose(T0_iter0 + xx_theta, T0_iter1, atol=1e-8, equal_nan=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0015974a-106a-4fc6-880f-ca7af1d84dba",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ds['xx_sst'] = xr.DataArray(xx_theta[0], dims=ds['rA'].dims, coords=ds['rA'].coords)\n",
    "\n",
    "p = ds.xx_sst.where(ds.hFacC[0]).plot(vmin = -.3, vmax = .3, cmap=cmap, add_colorbar=False)\n",
    "ax.set_title(r'$\\delta\\mathrm{SST}_0$', fontsize=30, pad=20)\n",
    "ax.set_ylabel('Latitude', fontsize=14)\n",
    "ax.set_xlabel('Longitude', fontsize=14)\n",
    "\n",
    "cbar = fig.colorbar(p, ax=ax)\n",
    "cbar.ax.tick_params(labelsize=16)\n",
    "cbar.ax.set_ylabel('Potential Temperature [degC]', fontsize=14)\n",
    "ax.tick_params(axis='both', labelsize=14)\n",
    "\n",
    "fig.set_size_inches(6, 5)\n",
    "fig.tight_layout()\n",
    "\n",
    "# fig.savefig('delta_sst.png', dpi=500, bbox_inches='tight', facecolor='white') # Vectorized PDF"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f546faf8-3f62-4cea-a5bf-f8eed2bf9129",
   "metadata": {},
   "source": [
    "We can repeat the process for the perturbations made to $\\mathrm{atemp}$. We find once again that the perturbations are all positive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aeb7bee4-f762-4f04-998a-11eb74466d42",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, axes = plt.subplots(2, 3)\n",
    "set_cbar = True\n",
    "for i, ax in enumerate(axes.ravel()):\n",
    "    fld = xx_atemp[::-1][i]\n",
    "\n",
    "    vmax = 2e-2 if set_cbar else np.nanmax(abs(fld))\n",
    "    vmin = -vmax\n",
    "\n",
    "    # Add the field to the dataset for convenient lat/lon axis ticks on 2D plots\n",
    "    ds['fld'] = xr.DataArray(fld, dims=ds['rA'].dims, coords=ds['rA'].coords)\n",
    "    p = ds.fld.where(ds.hFacC[0]).plot(ax=ax, vmin=vmin, vmax=vmax, cmap=cmap, add_colorbar=False)\n",
    "\n",
    "    ax.set_title(r'$\\delta\\mathrm{atemp}$' + ' (lag {} day)'.format(i), fontsize=16)\n",
    "\n",
    "    ax.set_xlabel('Longitude' if i >= 3 else '', fontsize=14)\n",
    "    ax.set_ylabel('Latitude' if i % 3 == 0 else '', fontsize=14)\n",
    "    \n",
    "cbar_ax = fig.add_axes([0.1, -0.05, 0.8, 0.03])  # Position [left, bottom, width, height]\n",
    "cbar = fig.colorbar(p, cax=cbar_ax, orientation='horizontal')\n",
    "cbar_ax.tick_params(labelsize=16)\n",
    "cbar.ax.set_xlabel('Air temperature [degK]', fontsize=14)\n",
    "\n",
    "fig.set_size_inches(10, 7)\n",
    "fig.tight_layout()\n",
    "\n",
    "#fig.savefig('dJdatemp.png', dpi=500, bbox_inches='tight', facecolor='white') # Vectorized PDF\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83946327-6a2c-4912-a064-d3a6b26b4f55",
   "metadata": {},
   "source": [
    "### Load diagnostic data for many optimization iterations\n",
    "At this point, one runs the model from the newly obtained control perturbations. We copy `ecco_ctrl_MIT_CE_000.opt0001` into the next run directory, `run/iter0001`, and read them into the model by setting `doMainUnpack` in `data.ctrl`. Running the model forward again, one may choose to compare the diagnostics generated by `iter0000` with those from `iter0001`. The user should also confirm that the total cost in `costfunction0001` is smaller  than that of `costfunction0000`. The optimization routine is repeated until the cost has been reduced by a desired amount. We have performed 10 optimization iterations and saved the diagnostics for each.\n",
    "\n",
    "To assess our assimilation experiment, we create a wrapper to `xmitgcm.open_mdsdataset` to concatenate diagnostic datasets from multiple optimization iterations along a new axis `ioptim`. Note that this function is not particularly robust, in that we use knowledge of the directory structure:\n",
    "\n",
    "```\n",
    "run/\n",
    "│\n",
    "└───iter0000/\n",
    "│   │   ...\n",
    "│   \n",
    "└───iter0001/\n",
    "│   │   ...\n",
    "│\n",
    "│   ...\n",
    "│ \n",
    "└───iter0009/\n",
    "    │   ...\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "3a04b19b-e2ec-48ed-89d7-ac39f0722e9e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "diagnostics from 10 optimization iterations loaded\n"
     ]
    }
   ],
   "source": [
    "def open_mdsdataset_optim(run_dir,\n",
    "                          nopts_max = None,\n",
    "                          iter_dir_pfx = 'iter',\n",
    "                          verbose=False,\n",
    "                          **open_mdsdataset_kwargs):\n",
    "    iter_dirs = np.sort(glob.glob(run_dir + iter_dir_pfx + '*/')).tolist()\n",
    "    iter_dirs = iter_dirs[:nopts_max]\n",
    "\n",
    "    ds_list = []\n",
    "    for this_iter_dir in iter_dirs:\n",
    "        if verbose: print(f'loading data from iter_dir={this_iter_dir}')\n",
    "        ds_i = xmitgcm.open_mdsdataset(this_iter_dir,\n",
    "                                       grid_dir = this_iter_dir,\n",
    "                                       **open_mdsdataset_kwargs)\n",
    "        ds_list.append(ds_i)\n",
    "        ds_i.close()\n",
    "    return xr.concat(ds_list, dim='ioptim')\n",
    "\n",
    "prefix = 'diags3d'\n",
    "\n",
    "ds = open_mdsdataset_optim(run_dir,\n",
    "                        prefix = [prefix],\n",
    "                        default_dtype=np.float32,\n",
    "                        delta_t=900,\n",
    "                        ref_date='1979-01-01 00:00:00'\n",
    "                            )\n",
    "ds['XC'] = xr.where(ds.XC > 180, ds.XC - 360, ds.XC)\n",
    "ds['XG'] = xr.where(ds.XG > 180, ds.XG - 360, ds.XG)\n",
    "\n",
    "nopts = len(ds.ioptim)\n",
    "print(f'diagnostics from {nopts} optimization iterations loaded')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0903294b-f795-46f4-9c9e-c010f18c34e9",
   "metadata": {},
   "source": [
    "### Plot the cost function reduction\n",
    "We find that from optimization iteration one to two, a considerable decrease in the cost $J$ is achieved. After a few more iterations, the cost plateaus. The cost reduction is an indicator of a successful assimilation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "e056984f-dac3-490d-ac6a-c4af02ddfd6c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "costs = []\n",
    "for ioptim in range(nopts):\n",
    "    run_dir_i = f'{run_dir}/iter{ioptim:04d}'\n",
    "    costfunction_filename = f'{run_dir_i}/costfunction{ioptim:04d}'\n",
    "    field_name = 'fc'\n",
    "    costs.append(grep_cost(run_dir_i, ioptim=ioptim))\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "x = np.arange(nopts)\n",
    "ax.plot(x, costs, 'k')#, alpha=.5)\n",
    "ax.scatter(x, costs, c='k')#, alpha=.5)\n",
    "ax.set_title(r'Cost function', fontsize=30, pad=20)\n",
    "ax.set_ylabel(r'$J$', fontsize=18)\n",
    "ax.set_xlabel('Iteration', fontsize=18)\n",
    "ax.semilogy()\n",
    "yticks = [1e7, 5e6, 1e6, 5e5]\n",
    "ax.set_yticks(yticks)\n",
    "ax.set_xticks(np.arange(nopts))\n",
    "ax.set_ylim(1e6, 4e7)\n",
    "ax.tick_params(axis='both', labelsize=16)\n",
    "fig.tight_layout()\n",
    "fig.set_size_inches(6, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b446c18c-639c-499a-a279-cb7e815494cf",
   "metadata": {},
   "source": [
    "### Visualize the misfit reduction\n",
    "Lastly, we can give a qualitative \"eye test\" to assure that the assimilation did what we expected by looking at the model SST on day 6 before and after optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "cf849af4-f18d-4e72-8620-4e57651a5ba7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# re-add the observational data to the dataset\n",
    "ds['data_sst'] = xr.DataArray(data_sst, dims=['time','YC','XC'])\n",
    "\n",
    "fig, ax = plot_model_data_misfit(ds.isel(ioptim=0))\n",
    "fig.suptitle('Iteration 0', fontsize=30, y = 1.1)\n",
    "\n",
    "fig, ax = plot_model_data_misfit(ds.isel(ioptim=9))\n",
    "fig.suptitle('Iteration 9', fontsize=30, y = 1.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec27ec9f-7455-4807-9369-607b75ca3270",
   "metadata": {},
   "source": [
    "Eureka💡! As we had hoped the model SST on day 6 looks much more similar to the observational data after optimization. Moreover, the spatial plot of the misfit is clearly nearer to zero almost everywhere. \n",
    "\n",
    "### Conclusion\n",
    "We demonstrated the workflows used to assimilate synthetic observational data into an unconstrained MITgcm model. Along the way, we investigated model diagnostics, sensitivity to controls, control perturbations, and cost function reduction across iterations. The reader is encouraged to play with different model parameters in `data`, explore other options for $J$ such as boxmean quantities of interest ([more info here](https://mitgcm.readthedocs.io/en/latest/ocean_state_est/ocean_state_est.html)), and further probe changes in model diagnostics between iteration 0 and 9 to understand exacly how the physics of the model changed in order to accomodate the data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79ec5150-f997-467c-8ae3-3ad7fbf368f6",
   "metadata": {},
   "source": [
    "### References\n",
    "Adcroft, A., Campin, J., Dutkiewicz, S., Evangelinos, C., Ferreira, D., Forget, G., et al. (2018). MITgcm User Manual. Zenodo. https://doi.org/10.5281/zenodo.3248738\n",
    "\n",
    "Loose, N., & Heimbach, P. (2021). Leveraging Uncertainty Quantification to Design Ocean Climate Observing Systems. *Journal of Advances in Modeling Earth Systems*, 13(4), e2020MS002386. https://doi.org/10.1029/2020MS002386\n"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.9"
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