|
| 1 | +{ |
| 2 | + "cells": [ |
| 3 | + { |
| 4 | + "cell_type": "markdown", |
| 5 | + "id": "a8e2583ad32cdf8", |
| 6 | + "metadata": {}, |
| 7 | + "source": [ |
| 8 | + "# Custom Grid Topology\n", |
| 9 | + "\n", |
| 10 | + "This notebook will showcase how to construct UXarray data structures from custom grid topology information, including how to convert existing Xarray data structures to UXarray." |
| 11 | + ] |
| 12 | + }, |
| 13 | + { |
| 14 | + "cell_type": "code", |
| 15 | + "execution_count": null, |
| 16 | + "id": "57e64b0ff76581ca", |
| 17 | + "metadata": {}, |
| 18 | + "outputs": [], |
| 19 | + "source": [ |
| 20 | + "import uxarray as ux\n", |
| 21 | + "import xarray as xr\n", |
| 22 | + "import numpy as np" |
| 23 | + ] |
| 24 | + }, |
| 25 | + { |
| 26 | + "cell_type": "markdown", |
| 27 | + "id": "4cd183a0-3658-4c68-9e08-ed4ff063a0ea", |
| 28 | + "metadata": {}, |
| 29 | + "source": [ |
| 30 | + "## Minimal Grid Definition\n", |
| 31 | + "\n", |
| 32 | + "The UGRID conventions require a minimal set of variables for representing a 2D unstructured grid. \n", |
| 33 | + "\n", |
| 34 | + "| **Variable** | **Shape** | **Description** |\n", |
| 35 | + "|--------------------------|--------------------------------|------------------------------------------------|\n", |
| 36 | + "| `node_lon` | `(n_node, )` | Longitude of the nodes that make up each face. |\n", |
| 37 | + "| `node_lat` | `(n_node, )` | Latitude of the nodes that make up each face. |\n", |
| 38 | + "| `face_node_connectivity` | `(n_face, n_max_face_nodes])` | Indices of the nodes that surround each face. |\n" |
| 39 | + ] |
| 40 | + }, |
| 41 | + { |
| 42 | + "cell_type": "markdown", |
| 43 | + "id": "072075f6-6b91-4e91-9c28-67bb9ee073ef", |
| 44 | + "metadata": {}, |
| 45 | + "source": [ |
| 46 | + "## Fixed Face Sizes\n", |
| 47 | + "\n", |
| 48 | + "For grids where each face has the same number of nodes, such as strictly triangular grids, each row in the `face_node_connectivity` array will contain the indices of nodes that surround each face, with no fill values. Below is an example of the node coordinates and connectivity required for representing a single triangle in the UGRID conventions." |
| 49 | + ] |
| 50 | + }, |
| 51 | + { |
| 52 | + "cell_type": "code", |
| 53 | + "execution_count": null, |
| 54 | + "id": "f608c0e2-9334-4e1e-aed4-d44b923a5566", |
| 55 | + "metadata": {}, |
| 56 | + "outputs": [], |
| 57 | + "source": [ |
| 58 | + "node_lon = np.array([-20.0, 0.0, 20.0])\n", |
| 59 | + "node_lat = np.array([-10.0, 10.0, -10.0])\n", |
| 60 | + "face_node_connectivity = np.array(\n", |
| 61 | + " [\n", |
| 62 | + " [0, 1, 2],\n", |
| 63 | + " ]\n", |
| 64 | + ")" |
| 65 | + ] |
| 66 | + }, |
| 67 | + { |
| 68 | + "cell_type": "markdown", |
| 69 | + "id": "f8e3b665-c225-44d6-81b1-80ad23a1b38d", |
| 70 | + "metadata": {}, |
| 71 | + "source": [ |
| 72 | + "These variables can be passed directly into the `Grid.from_topology()` class-method, which allows custom grid topology information. This is especially useful for cases where a specific grid format isn't directly supported. " |
| 73 | + ] |
| 74 | + }, |
| 75 | + { |
| 76 | + "cell_type": "code", |
| 77 | + "execution_count": null, |
| 78 | + "id": "b1b3fe63-28f1-4082-910f-8fa3179f1cf8", |
| 79 | + "metadata": {}, |
| 80 | + "outputs": [], |
| 81 | + "source": [ |
| 82 | + "uxgrid_tri = ux.Grid.from_topology(\n", |
| 83 | + " node_lon=node_lon, node_lat=node_lat, face_node_connectivity=face_node_connectivity\n", |
| 84 | + ")" |
| 85 | + ] |
| 86 | + }, |
| 87 | + { |
| 88 | + "cell_type": "code", |
| 89 | + "execution_count": null, |
| 90 | + "id": "d9846c0f-309b-4b8a-b355-98d23bfd5ce9", |
| 91 | + "metadata": {}, |
| 92 | + "outputs": [], |
| 93 | + "source": [ |
| 94 | + "uxgrid_tri.plot(title=\"Triangle\")" |
| 95 | + ] |
| 96 | + }, |
| 97 | + { |
| 98 | + "cell_type": "markdown", |
| 99 | + "id": "f96283a6-a6b8-40ae-99e5-860686fc580d", |
| 100 | + "metadata": {}, |
| 101 | + "source": [ |
| 102 | + "## Mixed Face Sizes\n", |
| 103 | + "\n", |
| 104 | + "For grids where each face does not have the same number of nodes, the `face_node_connectivity` array will have it's final dimension (`n_max_face_nodes`) set to the largest element shape. For example, a grid with triangles and quadrialterals will have a final dimension of 4. Any element that has less than the maximum number of nodes will be padded with a fill value. The `face_node_connectivity` array below showcases a basic grid with a single triangle and quadrilateral. Observe that the first row is set to `[0, 1, 2, -1]`, with the first three integers being the indices of the triangle corners, and the final value used as a fill value." |
| 105 | + ] |
| 106 | + }, |
| 107 | + { |
| 108 | + "cell_type": "code", |
| 109 | + "execution_count": null, |
| 110 | + "id": "43e13ad3-e020-464f-a14b-bbac8bed6bb5", |
| 111 | + "metadata": {}, |
| 112 | + "outputs": [], |
| 113 | + "source": [ |
| 114 | + "node_lon = np.array([-20.0, 0.0, 20.0, -20, -40])\n", |
| 115 | + "node_lat = np.array([-10.0, 10.0, -10.0, 10, -10])\n", |
| 116 | + "face_node_connectivity = np.array([[0, 1, 2, -1], [0, 1, 3, 4]])" |
| 117 | + ] |
| 118 | + }, |
| 119 | + { |
| 120 | + "cell_type": "markdown", |
| 121 | + "id": "c28d3bb0-b469-41e4-a250-5b8f5f2125a9", |
| 122 | + "metadata": {}, |
| 123 | + "source": [ |
| 124 | + "The `fill_value` parameter must be passed in when working with a mixed topology grid. " |
| 125 | + ] |
| 126 | + }, |
| 127 | + { |
| 128 | + "cell_type": "code", |
| 129 | + "execution_count": null, |
| 130 | + "id": "4669559c-5f79-47ed-a53f-6bf85b1eaea4", |
| 131 | + "metadata": {}, |
| 132 | + "outputs": [], |
| 133 | + "source": [ |
| 134 | + "uxgrid_tri_quad = ux.Grid.from_topology(\n", |
| 135 | + " node_lon=node_lon,\n", |
| 136 | + " node_lat=node_lat,\n", |
| 137 | + " face_node_connectivity=face_node_connectivity,\n", |
| 138 | + " fill_value=-1,\n", |
| 139 | + ")" |
| 140 | + ] |
| 141 | + }, |
| 142 | + { |
| 143 | + "cell_type": "code", |
| 144 | + "execution_count": null, |
| 145 | + "id": "e54be66c-d602-41c1-a966-efc4bb7a29c8", |
| 146 | + "metadata": {}, |
| 147 | + "outputs": [], |
| 148 | + "source": [ |
| 149 | + "uxgrid_tri_quad.plot(title=\"Triangle & Quad\")" |
| 150 | + ] |
| 151 | + }, |
| 152 | + { |
| 153 | + "cell_type": "markdown", |
| 154 | + "id": "36d09bd1-87cc-4b78-8d2d-8108ef61f7a2", |
| 155 | + "metadata": {}, |
| 156 | + "source": [ |
| 157 | + "## Working with Existing Xarray Structures\n", |
| 158 | + "\n", |
| 159 | + "The previous examples showcase how to create a `Grid` from custom topology. The follow sections will walk through how to match data to the `Grid`." |
| 160 | + ] |
| 161 | + }, |
| 162 | + { |
| 163 | + "cell_type": "markdown", |
| 164 | + "id": "0876cfed-16a2-4532-ab7e-60754c897a5f", |
| 165 | + "metadata": {}, |
| 166 | + "source": [ |
| 167 | + "### `xr.DataArray` to `ux.UxDataArray`\n", |
| 168 | + "\n", |
| 169 | + "Consider the previous example where we constructed the `uxgrid_tri` grid, consisting of a single triangle. Below is an example `xr.DataArray` containing four temperature values. " |
| 170 | + ] |
| 171 | + }, |
| 172 | + { |
| 173 | + "cell_type": "code", |
| 174 | + "execution_count": null, |
| 175 | + "id": "0d7dce48-e6f4-4bba-8b25-961139fb07b5", |
| 176 | + "metadata": {}, |
| 177 | + "outputs": [], |
| 178 | + "source": [ |
| 179 | + "xrda_temp = xr.DataArray(\n", |
| 180 | + " name=\"temp\",\n", |
| 181 | + " data=np.array(\n", |
| 182 | + " [\n", |
| 183 | + " [100, 105, 108, 109],\n", |
| 184 | + " ]\n", |
| 185 | + " ).T,\n", |
| 186 | + " dims=[\"time\", \"cell\"],\n", |
| 187 | + ")\n", |
| 188 | + "xrda_temp" |
| 189 | + ] |
| 190 | + }, |
| 191 | + { |
| 192 | + "cell_type": "markdown", |
| 193 | + "id": "41f67fbad5c3e485", |
| 194 | + "metadata": {}, |
| 195 | + "source": [ |
| 196 | + "The original dimension must be mapped to their UGRID equivalent. \n", |
| 197 | + "\n", |
| 198 | + "| **Data Mapping** | **UGRID Dimension Name** |\n", |
| 199 | + "|------------------|--------------------------|\n", |
| 200 | + "| Faces | n_face |\n", |
| 201 | + "| Edges | n_edge |\n", |
| 202 | + "| Nodes | n_node |\n", |
| 203 | + "\n", |
| 204 | + "\n", |
| 205 | + "In the example above, the `cell` dimension corresponds to the faces of the grid, meaning we want to translate the dimension to `n_face`\n", |
| 206 | + "\n" |
| 207 | + ] |
| 208 | + }, |
| 209 | + { |
| 210 | + "cell_type": "code", |
| 211 | + "execution_count": null, |
| 212 | + "id": "db7ea793-4f8e-4ae9-beec-1bfb0080d79f", |
| 213 | + "metadata": {}, |
| 214 | + "outputs": [], |
| 215 | + "source": [ |
| 216 | + "ugrid_dims = {\"cell\": \"n_face\"}" |
| 217 | + ] |
| 218 | + }, |
| 219 | + { |
| 220 | + "cell_type": "markdown", |
| 221 | + "id": "da24da79813502a5", |
| 222 | + "metadata": {}, |
| 223 | + "source": [ |
| 224 | + "The `UxDataArray.from_xarray()` takes in a user-defined `Grid` in addition to the original `xr.DataArray` and UGRID dimension mapping and returns a `UxDataArray`" |
| 225 | + ] |
| 226 | + }, |
| 227 | + { |
| 228 | + "cell_type": "code", |
| 229 | + "execution_count": null, |
| 230 | + "id": "797993ac-0e83-437b-a950-704f31f4eae4", |
| 231 | + "metadata": {}, |
| 232 | + "outputs": [], |
| 233 | + "source": [ |
| 234 | + "uxda_temp = ux.UxDataArray.from_xarray(xrda_temp, uxgrid_tri, ugrid_dims)\n", |
| 235 | + "uxda_temp" |
| 236 | + ] |
| 237 | + }, |
| 238 | + { |
| 239 | + "cell_type": "markdown", |
| 240 | + "id": "67131fdf-3431-47ea-8e9c-0409300d7667", |
| 241 | + "metadata": {}, |
| 242 | + "source": [ |
| 243 | + "### `xr.Dataset` to `ux.UxDataset`\n", |
| 244 | + "\n", |
| 245 | + "More commonly, you may have an entire `xr.Dataset` that contains data variables. " |
| 246 | + ] |
| 247 | + }, |
| 248 | + { |
| 249 | + "cell_type": "code", |
| 250 | + "execution_count": null, |
| 251 | + "id": "e967c9466b3cb25d", |
| 252 | + "metadata": {}, |
| 253 | + "outputs": [], |
| 254 | + "source": [ |
| 255 | + "xrda_vorticity = xr.DataArray(\n", |
| 256 | + " name=\"vorticity\",\n", |
| 257 | + " data=np.array(\n", |
| 258 | + " [\n", |
| 259 | + " [1, 2, 3, 4],\n", |
| 260 | + " [5, 6, 7, 8],\n", |
| 261 | + " [9, 10, 11, 12],\n", |
| 262 | + " ]\n", |
| 263 | + " ).T,\n", |
| 264 | + " dims=[\"time\", \"vertex\"],\n", |
| 265 | + ")" |
| 266 | + ] |
| 267 | + }, |
| 268 | + { |
| 269 | + "cell_type": "markdown", |
| 270 | + "id": "86c9a24a4320d7d0", |
| 271 | + "metadata": {}, |
| 272 | + "source": [ |
| 273 | + "In this example, we have a cell-centered `temp` and vertex-centered `vorticity` variable. " |
| 274 | + ] |
| 275 | + }, |
| 276 | + { |
| 277 | + "cell_type": "code", |
| 278 | + "execution_count": null, |
| 279 | + "id": "906532aa-acb3-43c4-95f9-ef9d29312865", |
| 280 | + "metadata": {}, |
| 281 | + "outputs": [], |
| 282 | + "source": [ |
| 283 | + "ds = xr.Dataset(data_vars={\"temp\": xrda_temp, \"vorticity\": xrda_vorticity})\n", |
| 284 | + "ds" |
| 285 | + ] |
| 286 | + }, |
| 287 | + { |
| 288 | + "cell_type": "markdown", |
| 289 | + "id": "bb01a75189469712", |
| 290 | + "metadata": {}, |
| 291 | + "source": [ |
| 292 | + "We must now include an additional entry into our `ugrid_dims` dictionary for our vertex-centered data variable." |
| 293 | + ] |
| 294 | + }, |
| 295 | + { |
| 296 | + "cell_type": "code", |
| 297 | + "execution_count": null, |
| 298 | + "id": "a266b291-c189-40a3-955b-d64dc937d5c9", |
| 299 | + "metadata": {}, |
| 300 | + "outputs": [], |
| 301 | + "source": [ |
| 302 | + "ugrid_dims = {\"cell\": \"n_face\", \"vertex\": \"n_node\"}" |
| 303 | + ] |
| 304 | + }, |
| 305 | + { |
| 306 | + "cell_type": "code", |
| 307 | + "execution_count": null, |
| 308 | + "id": "8a9b3bf5-38bb-4e9a-8890-4d540b9f62b7", |
| 309 | + "metadata": {}, |
| 310 | + "outputs": [], |
| 311 | + "source": [ |
| 312 | + "uxds = ux.UxDataset.from_xarray(ds=ds, uxgrid=uxgrid_tri, ugrid_dims=ugrid_dims)" |
| 313 | + ] |
| 314 | + }, |
| 315 | + { |
| 316 | + "cell_type": "markdown", |
| 317 | + "id": "7d0b1326", |
| 318 | + "metadata": {}, |
| 319 | + "source": [ |
| 320 | + "uxds now has two `UxDataArray` objects, one for the cell-centered data `temp` and one for the vertex-centered data `vorticity`. There are 4 time steps 0, 1, 2, and 3. Values for time step 0 are shown below." |
| 321 | + ] |
| 322 | + }, |
| 323 | + { |
| 324 | + "cell_type": "code", |
| 325 | + "execution_count": null, |
| 326 | + "id": "992a409a", |
| 327 | + "metadata": {}, |
| 328 | + "outputs": [], |
| 329 | + "source": [ |
| 330 | + "uxds[\"vorticity\"][0]" |
| 331 | + ] |
| 332 | + } |
| 333 | + ], |
| 334 | + "metadata": { |
| 335 | + "kernelspec": { |
| 336 | + "display_name": "uxarray_env3.12", |
| 337 | + "language": "python", |
| 338 | + "name": "python3" |
| 339 | + }, |
| 340 | + "language_info": { |
| 341 | + "codemirror_mode": { |
| 342 | + "name": "ipython", |
| 343 | + "version": 3 |
| 344 | + }, |
| 345 | + "file_extension": ".py", |
| 346 | + "mimetype": "text/x-python", |
| 347 | + "name": "python", |
| 348 | + "nbconvert_exporter": "python", |
| 349 | + "pygments_lexer": "ipython3", |
| 350 | + "version": "3.12.7" |
| 351 | + } |
| 352 | + }, |
| 353 | + "nbformat": 4, |
| 354 | + "nbformat_minor": 5 |
| 355 | +} |
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