stress_factor_shape.ipynb 1.89 MB
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 Oscar Corvi committed Jul 15, 2021 1 2 3 4 { "cells": [ { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 5 "id": "consecutive-compromise", Oscar Corvi committed Jul 15, 2021 6 7 8 9 10 11 12 "metadata": {}, "source": [ "# **Mathematical shape of the stress factor function**" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 13 "id": "sufficient-kenya", Oscar Corvi committed Jul 15, 2021 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Part I - Methodology \n", "\n", "## Motivation \n", "\n", "### Theoretical background\n", "\n", "Different mathematical shapes of the stress factor can be found in the litterature, from simplistic linear ones (Martens et al., 2017) to more exotic and complex shapes (Sellers et al., 2007). The present notebook does not aim at exploring all the different mathmatical shapes possible for the stress factor arising from the literature. We will limit our investigation to the three most commonly encountered shapes : \n", "1. Linear : \n", "\\n", "F(\\theta) = \n", "\\begin{cases} \n", "0 & \\theta < \\theta_4\\\\\n", "\\frac{\\theta-\\theta_4}{\\theta_3 - \\theta_4} & \\theta_4 < \\theta < \\theta_3\\\\\n", "1 & \\theta > \\theta_3\n", "\\end{cases}\n", "\\n", "\n", "2. Exponential concave :\n", "\\n", "F(\\theta) = \n", "\\begin{cases} \n", "0 & \\theta < \\theta_4\\\\\n", "a.exp(b.\\theta) & \\theta_4 < \\theta < \\theta_3, b > 0\\\\\n", "1 & \\theta > \\theta_3\n", "\\end{cases}\n", "\\n", "\n", "3. Exponential convexe :\n", "\\n", "F(\\theta) = \n", "\\begin{cases} \n", "0 & \\theta < \\theta_4\\\\\n", "a.exp(b.\\theta) & \\theta_4 < \\theta < \\theta_3, b < 0\\\\\n", "1 & \\theta > \\theta_3\n", "\\end{cases}\n", "\\n", "\n", "### Modelling experiements\n", "\n", "Different experiments are carried out to compare the different models and assess their behavior: \n", "1. All models are calibrated for a single year and their ability to reproduce an observed time serie is assessed\n", "2. Their prediction capability is evaluated by randomly taking one or several years of data from the Howard Springs dataset, calibrating the model for this specific year and predicting the evapo-transpiration time serie for the other years. \n", "3. The same procedure is repeated across different sites in Australia" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 67 "id": "headed-theorem", Oscar Corvi committed Jul 15, 2021 68 69 70 71 72 73 74 "metadata": {}, "source": [ "# Part II - Functions set up" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 75 "id": "distant-antarctica", Oscar Corvi committed Jul 15, 2021 76 77 78 79 80 81 82 83 "metadata": {}, "source": [ "## Importing relevant packages" ] }, { "cell_type": "code", "execution_count": 1, Oscar Corvi committed Jul 15, 2021 84 "id": "adverse-croatia", Oscar Corvi committed Jul 15, 2021 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING (aesara.link.c.cmodule): install mkl with conda install mkl-service: No module named 'mkl'\n", "WARNING (aesara.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" ] } ], "source": [ "# data manipulation and plotting\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from matplotlib._layoutgrid import plot_children\n", "from collections import OrderedDict\n", "from IPython.display import display\n", "import os # to look into the other folders of the project\n", "import importlib.util # to open the .py files written somewhere else\n", "#sns.set_theme(style=\"whitegrid\")\n", "\n", "# Sympy and sympbolic mathematics\n", "from sympy import (asin, cos, diff, Eq, exp, init_printing, log, pi, sin, \n", " solve, sqrt, Symbol, symbols, tan, Abs)\n", "from sympy.physics.units import convert_to\n", "init_printing() \n", "from sympy.printing import StrPrinter\n", "from sympy import Piecewise\n", "StrPrinter._print_Quantity = lambda self, expr: str(expr.abbrev) # displays short units (m instead of meter)\n", "from sympy.printing.aesaracode import aesara_function\n", "from sympy.physics.units import * # Import all units and dimensions from sympy\n", "from sympy.physics.units.systems.si import dimsys_SI, SI\n", "\n", "# for ESSM, environmental science for symbolic math, see https://github.com/environmentalscience/essm\n", "from essm.variables._core import BaseVariable, Variable\n", "from essm.equations import Equation\n", "from essm.variables.units import derive_unit, SI, Quantity\n", "from essm.variables.utils import (extract_variables, generate_metadata_table, markdown, \n", " replace_defaults, replace_variables, subs_eq)\n", "from essm.variables.units import (SI_BASE_DIMENSIONS, SI_EXTENDED_DIMENSIONS, SI_EXTENDED_UNITS,\n", " derive_unit, derive_baseunit, derive_base_dimension)\n", "\n", "# For netCDF\n", "import netCDF4\n", "import numpy as np\n", "import xarray as xr\n", "import warnings\n", "from netCDF4 import Dataset\n", "\n", "# For regressions\n", "from sklearn.linear_model import LinearRegression\n", "\n", "# Deactivate unncessary warning messages related to a bug in Numpy\n", "warnings.simplefilter(action='ignore', category=FutureWarning)\n", "\n", "# for calibration\n", "from scipy import optimize\n", "\n", "from random import random" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 149 "id": "early-excuse", Oscar Corvi committed Jul 15, 2021 150 151 152 153 154 155 156 157 "metadata": {}, "source": [ "## Path of the different files (pre-defined python functions, sympy equations, sympy variables)" ] }, { "cell_type": "code", "execution_count": 2, Oscar Corvi committed Jul 15, 2021 158 "id": "right-degree", Oscar Corvi committed Jul 15, 2021 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 "metadata": { "tags": [ "parameters" ] }, "outputs": [], "source": [ "path_variable = '../../theory/pyFile_storage/theory_variable.py'\n", "path_equation = '../../theory/pyFile_storage/theory_equation.py' \n", "path_analysis_functions = '../../theory/pyFile_storage/analysis_functions.py'\n", "path_data = '../../../data/eddycovdata/'\n", "dates_fPAR = '../../../data/fpar_howard_spring/dates_v5'\n", "\n", "timeSerie_oneSite_oneYear = 'timeSerie_oneSite_oneYear.png'\n", "inverseModelling = \"inverseModelling.png\"\n", "Influence_atmo_E_dry = \"Influence_atmo_E_dry.png\"\n", "Influence_atmo_E_wet = \"Influence_atmo_E_wet.png\"\n", "Influence_atmo_rel_dry = \"Influence_atmo_rel_dry.png\"\n", "Influence_atmo_rel_wet = \"Influence_atmo_rel_wet.png\"\n", "sensitivity_parameters = \"sensitivity_parameters.png\"\n", "statistical_assessment = \"statistical_assessment.png\"\n", "different_sites = \"different_sites.png\"" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 185 "id": "centered-panama", Oscar Corvi committed Jul 15, 2021 186 187 188 189 190 191 192 193 "metadata": {}, "source": [ "## Importing the sympy variables and equations defined in the theory.ipynb notebook" ] }, { "cell_type": "code", "execution_count": 3, Oscar Corvi committed Jul 15, 2021 194 "id": "guided-weekend", Oscar Corvi committed Jul 15, 2021 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "theta_sat\n", "theta_res\n", "alpha\n", "n\n", "m\n", "S_mvg\n", "theta\n", "h\n", "S\n", "theta_4\n", "theta_3\n", "theta_2\n", "theta_1\n", "L\n", "Mw\n", "Pv\n", "Pvs\n", "R\n", "T\n", "c1\n", "T0\n", "Delta\n", "E\n", "G\n", "H\n", "Rn\n", "LE\n", "gamma\n", "alpha_PT\n", "c_p\n", "w\n", "kappa\n", "z\n", "u_star\n", "VH\n", "d\n", "z_om\n", "z_oh\n", "r_a\n", "g_a\n", "r_s\n", "g_s\n", "c1_e\n", "c2_e\n", "e\n", "T_min\n", "T_max\n", "RH_max\n", "RH_min\n", "e_a\n", "e_s\n", "iv_T\n", "T_kv\n", "P\n", "rho_a\n", "VPD\n", "eq_m_n\n", "eq_MVG_neg_case\n", "eq_MVG\n", "eq_sat_degree\n", "eq_MVG_h\n", "eq_h_FC\n", "eq_theta_4_3\n", "eq_theta_2_1\n", "eq_water_stress_simple\n", "eq_Pvs_T\n", "eq_Delta\n", "eq_PT\n", "eq_PM\n", "eq_PM_VPD\n", "eq_PM_g\n", "eq_PM_inv\n" ] } ], "source": [ "for code in [path_variable,path_equation]:\n", " name_code = code[-20:-3]\n", " spec = importlib.util.spec_from_file_location(name_code, code)\n", " mod = importlib.util.module_from_spec(spec)\n", " spec.loader.exec_module(mod)\n", " names = getattr(mod, '__all__', [n for n in dir(mod) if not n.startswith('_')])\n", " glob = globals()\n", " for name in names:\n", " print(name)\n", " glob[name] = getattr(mod, name)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 291 "id": "hidden-westminster", Oscar Corvi committed Jul 15, 2021 292 293 294 295 296 297 298 299 "metadata": {}, "source": [ "## Importing the performance assessment functions defined in the analysis_function.py file" ] }, { "cell_type": "code", "execution_count": 4, Oscar Corvi committed Jul 15, 2021 300 "id": "polish-invention", Oscar Corvi committed Jul 15, 2021 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "AIC\n", "AME\n", "BIC\n", "CD\n", "CP\n", "IoA\n", "KGE\n", "MAE\n", "MARE\n", "ME\n", "MRE\n", "MSRE\n", "MdAPE\n", "NR4MS4E\n", "NRMSE\n", "NS\n", "NSC\n", "PDIFF\n", "PEP\n", "R4MS4E\n", "RAE\n", "RMSE\n", "RVE\n", "np\n", "nt\n" ] } ], "source": [ "for code in [path_analysis_functions]:\n", " name_code = code[-20:-3]\n", " spec = importlib.util.spec_from_file_location(name_code, code)\n", " mod = importlib.util.module_from_spec(spec)\n", " spec.loader.exec_module(mod)\n", " names = getattr(mod, '__all__', [n for n in dir(mod) if not n.startswith('_')])\n", " glob = globals()\n", " for name in names:\n", " print(name)\n", " glob[name] = getattr(mod, name)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 350 "id": "level-contrast", Oscar Corvi committed Jul 15, 2021 351 352 353 354 355 356 357 "metadata": {}, "source": [ "## Data import, preprocess and shape for the computations" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 358 "id": "powerful-arizona", Oscar Corvi committed Jul 15, 2021 359 360 361 362 363 364 365 366 367 368 "metadata": {}, "source": [ "### Get the different files where data are stored\n", "\n", "Eddy-covariance data from the OzFlux network are stored in **.nc** files (NetCDF4 files) which is roughly a panda data frame with meta-data (see https://www.unidata.ucar.edu/software/netcdf/ for more details about NetCDF4 file format). fPAR data are stored in **.txt** files" ] }, { "cell_type": "code", "execution_count": 5, Oscar Corvi committed Jul 15, 2021 369 "id": "dated-performance", Oscar Corvi committed Jul 15, 2021 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['../../../data/eddycovdata/fpar_adelaide_v5.txt', '../../../data/eddycovdata/fpar_daly_v5.txt', '../../../data/eddycovdata/fpar_dry_v5.txt', '../../../data/eddycovdata/fpar_howard_v5.txt', '../../../data/eddycovdata/fpar_sturt_v5.txt']\n", "['../../../data/eddycovdata/AdelaideRiver_L4.nc', '../../../data/eddycovdata/DalyUncleared_L4.nc', '../../../data/eddycovdata/DryRiver_L4.nc', '../../../data/eddycovdata/HowardSprings_L4.nc', '../../../data/eddycovdata/SturtPlains_L4.nc']\n" ] } ], "source": [ "fPAR_files = []\n", "eddy_files = []\n", "\n", "for file in os.listdir(path_data):\n", " if file.endswith(\".txt\"):\n", " fPAR_files.append(os.path.join(path_data, file))\n", " elif file.endswith(\".nc\"):\n", " eddy_files.append(os.path.join(path_data, file))\n", " \n", "fPAR_files.sort()\n", "print(fPAR_files)\n", "eddy_files.sort()\n", "print(eddy_files)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 399 "id": "steady-thought", Oscar Corvi committed Jul 15, 2021 400 401 402 403 404 405 406 407 408 "metadata": {}, "source": [ "### Define and test a function that process the fPAR data\n", "In the **.txt** files, only one value per month is given for the fPAR. The following function takes one .txt file containing data about the fPAR coefficients, and the related dates, stored in the a seperate file. The fPAR data (date and coefficients) are cleaned (good string formatting), mapped together and averaged to output one value per month (the fPAR measurement period doesn't spans the measurement period of the eddy covariance data)" ] }, { "cell_type": "code", "execution_count": 6, Oscar Corvi committed Jul 15, 2021 409 "id": "electric-paraguay", Oscar Corvi committed Jul 15, 2021 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 "metadata": {}, "outputs": [], "source": [ "def fPAR_data_process(fPAR_file,dates_fPAR):\n", " \n", " fparv5_dates = np.genfromtxt(dates_fPAR, dtype='str', delimiter=',')\n", " fparv5_dates = pd.to_datetime(fparv5_dates[:,1], format=\"%Y%m\")\n", " dates_pd = pd.date_range(fparv5_dates[0], fparv5_dates[-1], freq='MS')\n", "\n", " fparv5_howard = np.loadtxt(fPAR_file,delimiter=',', usecols=3 )\n", " fparv5_howard[fparv5_howard == -999] = np.nan\n", " fparv5_howard_pd = pd.Series(fparv5_howard, index = fparv5_dates)\n", " fparv5_howard_pd = fparv5_howard_pd.resample('MS').max()\n", "\n", " # convert fparv5_howard_pd to dataframe\n", " fPAR_pd = pd.DataFrame(fparv5_howard_pd)\n", " fPAR_pd = fPAR_pd.rename(columns={0:\"fPAR\"})\n", " fPAR_pd.index = fPAR_pd.index.rename(\"time\")\n", "\n", " # convert fPAR_pd to xarray to aggregate the data\n", " fPAR_xr = fPAR_pd.to_xarray()\n", " fPAR_agg = fPAR_xr.fPAR.groupby('time.month').max()\n", "\n", " # convert back to dataframe\n", " fPAR_pd = fPAR_agg.to_dataframe()\n", " Month = np.arange(1,13)\n", " Month_df = pd.DataFrame(Month)\n", " Month_df.index = fPAR_pd.index\n", " Month_df = Month_df.rename(columns={0:\"Month\"})\n", "\n", " fPAR_mon = pd.concat([fPAR_pd,Month_df], axis = 1)\n", " \n", " return(fPAR_mon)" ] }, { "cell_type": "code", "execution_count": 7, Oscar Corvi committed Jul 15, 2021 448 "id": "intended-merchant", Oscar Corvi committed Jul 15, 2021 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Takes two dataframes as input (one containing the fPAR data, the other containing the eddy-covariance data) and returns a data frame where the fPAR monthly values have been scaled to the time scale of the eddy covariance data" ] }, { "cell_type": "code", "execution_count": 8, Oscar Corvi committed Jul 15, 2021 584 "id": "capable-melbourne", Oscar Corvi committed Jul 15, 2021 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 "metadata": {}, "outputs": [], "source": [ "def fPARSet(df_add, fPAR_pd):\n", " \n", " # construct the time serie of the fPAR coefficients\n", " dummy_len = df_add[\"Fe\"].size\n", " fPAR_val = np.zeros((dummy_len,))\n", " \n", " dummy_pd = df_add\n", " dummy_pd.reset_index(inplace=True)\n", " dummy_pd.index=dummy_pd.time\n", " \n", " month_pd = dummy_pd['time'].dt.month\n", " \n", " for i in range(dummy_len):\n", " current_month = month_pd.iloc[i]\n", " line_fPAR = fPAR_pd[fPAR_pd['Month'] == current_month]\n", " fPAR_val[i] = line_fPAR['fPAR']\n", " \n", " # transform fPAR_val into dataframe to concatenate to df:\n", " fPAR = pd.DataFrame(fPAR_val, index = df_add.index)\n", " df_add = pd.concat([df_add,fPAR], axis = 1)\n", " df_add = df_add.rename(columns = {0:\"fPAR\"})\n", " \n", " return(df_add)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 615 "id": "successful-beach", Oscar Corvi committed Jul 15, 2021 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 "metadata": {}, "source": [ "### DataChose function\n", "\n", "Function taking the raw netcdf4 data file from the eddy covariance measurement and shape it such that it can be used for the computations. Only relevant variables are kept (latent heat flux, net radiation, ground heat flux, soil water content, wind speed, air temperature, VPD, bed shear stress). The desired data period is selected and is reshaped at the desired time scale (daily by default). Uses the fPARSet function defined above\n", "\n", "List of variable abbreviation : \n", "* Rn : Net radiation flux\n", "* G : Ground heat flux \n", "* Sws : soil moisture\n", "* Ta : Air temperature\n", "* RH : Relative humidity\n", "* W : Wind speed\n", "* E : measured evaporation\n", "* VPD : Vapour pressure deficit" ] }, { "cell_type": "code", "execution_count": 9, Oscar Corvi committed Jul 15, 2021 636 "id": "median-boards", Oscar Corvi committed Jul 15, 2021 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 "metadata": {}, "outputs": [], "source": [ "def DataChose(ds_ref, period_sel, fPAR_given, Freq = \"D\", sel_period_flag = True):\n", " \"\"\"Take subset of dataset if Flag == True, entire dataset else\n", " \n", " ds_ref: xarray object to be considered as the ref for selecting attributes\n", " agg_flag: aggregate the data at daily time scale if true\n", " Flag: select specific period if true (by default)\n", " period: time period to be selected\n", " ----------\n", " Method : \n", " - transform the xarray in panda dataframe for faster iteration\n", " - keep only the necessary columns : Fe, Fn, Fg, Ws, Sws, Ta, ustar, RH\n", " - transform / create new variables : Temperature in °C, T_min/T_max, RH_min/RH_max\n", " - create the Data vector (numpy arrays)\n", " - create back a xarray \n", " - return an xarray\n", " ----------\n", " \n", " Returns an xarray and a Data vector\n", " \"\"\"\n", " \n", " if sel_period_flag:\n", " df = ds_ref.sel(time = period_sel) \n", " # nameXarray_output = period + \"_\" + nameXarray_output\n", " else : \n", " df = ds_ref\n", " \n", " # keep only the columns of interest\n", " df = df[[\"Fe\",\"Fn\",\"Fg\",\"Ws\",\"Sws\",\"Ta\",\"ustar\",\"RH\", \"VPD\",\"ps\"]]\n", " \n", " # convert to dataframe\n", " df = df.to_dataframe()\n", " \n", " # aggregate following the rule stated in freq\n", " pd_Tmin = df.Ta.groupby([pd.Grouper(level = \"latitude\"), pd.Grouper(level = \"longitude\"), pd.Grouper(level = \"time\", freq = Freq)]).min()\n", " \n", " pd_Tmax = df.Ta.groupby([pd.Grouper(level = \"latitude\"), pd.Grouper(level = \"longitude\"), pd.Grouper(level = \"time\", freq = Freq)]).max()\n", " \n", " pd_RHmin = df.RH.groupby([pd.Grouper(level = \"latitude\"), pd.Grouper(level = \"longitude\"), pd.Grouper(level = \"time\", freq = Freq)]).min()\n", " \n", " pd_RHmax = df.RH.groupby([pd.Grouper(level = \"latitude\"), pd.Grouper(level = \"longitude\"), pd.Grouper(level = \"time\", freq = Freq)]).max()\n", " \n", " df = df.groupby([pd.Grouper(level = \"latitude\"), pd.Grouper(level = \"longitude\"), pd.Grouper(level = \"time\", freq = Freq)]).mean()\n", " df = pd.DataFrame(df)\n", " \n", " pd_Tmin = pd.DataFrame(pd_Tmin, index = df.index)\n", " pd_Tmin = pd_Tmin.rename(columns = {\"Ta\":\"Ta_min\"})\n", " \n", " pd_Tmax = pd.DataFrame(pd_Tmax, index = df.index)\n", " pd_Tmax = pd_Tmax.rename(columns = {\"Ta\":\"Ta_max\"})\n", " \n", " pd_RHmin = pd.DataFrame(pd_RHmin, index = df.index)\n", " pd_RHmin = pd_RHmin.rename(columns = {\"RH\":\"RH_min\"})\n", " \n", " pd_RHmax = pd.DataFrame(pd_RHmax, index = df.index)\n", " pd_RHmax = pd_RHmax.rename(columns = {\"RH\":\"RH_max\"})\n", " \n", " df = pd.concat([df,pd_Tmin,pd_Tmax,pd_RHmin,pd_RHmax],axis = 1)\n", " \n", " # convert data to the good units : \n", " df[\"Fe\"] = df[\"Fe\"]/2.45e6 # divide by latent heat of vaporization\n", " df[\"Ta\"] = df[\"Ta\"]+273 # convert to kelvin\n", " df[\"VPD\"] = df[\"VPD\"]*1000 # convert from kPa to Pa\n", " \n", " # construct the time serie of the fPAR coefficients\n", " df = fPARSet(df,fPAR_given)\n", " \n", " # initialise array for the error\n", " Error_obs = np.zeros((df.Fe.size,))\n", " \n", " for i in range(df.Fe.size):\n", " size_window_left, size_window_right = min(i,7),min(df.Fe.size - i-1, 7)\n", " #print(size_window_left, size_window_right)\n", " sub_set = df.Fe[i-size_window_left : i+size_window_right].to_numpy()\n", " mean_set = np.mean(sub_set)\n", " sdt_set = np.std(sub_set)\n", " error_obs = 2*sdt_set\n", " Error_obs[i] = error_obs\n", " \n", " ErrorObs = pd.DataFrame(Error_obs, index = df.index)\n", " \n", " df = pd.concat([df,ErrorObs], axis = 1)\n", " df = df.rename(columns = {0:\"error\"})\n", "\n", " \n", " return(df)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 729 "id": "utility-astronomy", Oscar Corvi committed Jul 15, 2021 730 731 732 733 734 735 736 737 "metadata": {}, "source": [ "## Compile the different functions defined in the symbolic domain\n", "All functions defined with sympy and ESSM are defined in the symbolic domain. In order to be efficiently evaluated, they need to be vectorized to allow computations with numpu arrays. We use the *aesara* printing compiler from the sympy package. Note that this printer replace the older one (*theano*) which is deprecated. A comparison of the performances between the two packages can be found in the aesara repository." ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 738 "id": "cathedral-pilot", Oscar Corvi committed Jul 15, 2021 739 740 741 742 743 744 745 746 "metadata": {}, "source": [ "### Water stress functions" ] }, { "cell_type": "code", "execution_count": 10, Oscar Corvi committed Jul 15, 2021 747 "id": "split-message", Oscar Corvi committed Jul 15, 2021 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 "metadata": {}, "outputs": [], "source": [ "def rising_slope_compiled():\n", " \"\"\"Compile the slope of the function between theta 4 and theta 3\"\"\"\n", " \n", " rising_slope = aesara_function([theta,theta_3, theta_4], [eq_theta_4_3.rhs], dims = {theta:1, theta_3:1, theta_4:1})\n", " \n", " return(rising_slope)\n", "\n", "def desc_slope_compiled():\n", " \"\"\"Compile the slope of the function between theta 2 and theta 1\"\"\"\n", " \n", " desc_slope = aesara_function([theta,theta_1, theta_2], [eq_theta_2_1.rhs], dims = {theta:1, theta_1:1, theta_2:1})\n", " \n", " return(desc_slope)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 768 "id": "circular-midnight", Oscar Corvi committed Jul 15, 2021 769 770 771 772 773 774 775 776 "metadata": {}, "source": [ "### Soil water potential" ] }, { "cell_type": "code", "execution_count": 11, Oscar Corvi committed Jul 15, 2021 777 "id": "vital-physiology", Oscar Corvi committed Jul 15, 2021 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 "metadata": {}, "outputs": [], "source": [ "def relative_saturation_compiled(ThetaRes, ThetaSat):\n", " \"\"\"Compile the relative saturation function of a soil\"\"\"\n", " Dict_value = {theta_res : ThetaRes, theta_sat : ThetaSat}\n", " \n", " S_mvg_func = aesara_function([theta], [eq_sat_degree.rhs.subs(Dict_value)], dims = {theta:1})\n", " \n", " return(S_mvg_func)" ] }, { "cell_type": "code", "execution_count": 12, Oscar Corvi committed Jul 15, 2021 793 "id": "resident-centre", Oscar Corvi committed Jul 15, 2021 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 "metadata": {}, "outputs": [], "source": [ "def Psi_compiled(alphaVal, nVal):\n", " \"\"\"Compile the soil water retention function as function of theta\"\"\"\n", " mVal = 1-1/nVal\n", " \n", " Dict_value = {alpha : alphaVal, n : nVal, m : mVal}\n", " \n", " Psi_function = aesara_function([S_mvg], [eq_MVG_h.rhs.subs(Dict_value)], dims = {S_mvg:1})\n", " \n", " return(Psi_function)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 810 "id": "previous-hobby", Oscar Corvi committed Jul 15, 2021 811 812 813 814 815 816 817 818 "metadata": {}, "source": [ "### Penman-Monteith" ] }, { "cell_type": "code", "execution_count": 13, Oscar Corvi committed Jul 15, 2021 819 "id": "single-execution", Oscar Corvi committed Jul 15, 2021 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 "metadata": {}, "outputs": [], "source": [ "def Delta_compiled():\n", " \"\"\"Compile the Delta function\"\"\"\n", " \n", " # creating the dictionnary with all default values from the above defined constants\n", " var_dict = Variable.__defaults__.copy()\n", " \n", " # computing delta values out of temperature values (slope of the water pressure curve)\n", " Delta_func = aesara_function([T],[eq_Delta.rhs.subs(var_dict)], dims = {T:1})\n", " \n", " return(Delta_func)" ] }, { "cell_type": "code", "execution_count": 14, Oscar Corvi committed Jul 15, 2021 838 "id": "special-celebration", Oscar Corvi committed Jul 15, 2021 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 "metadata": {}, "outputs": [], "source": [ "def VH_func_compiled(z_val):\n", " \"\"\"Compute the vegetation height function\n", " --------------------------------------------------------\n", " z : height of the measurements (m)\n", " kappa : Von Karman constant\n", " \n", " w : wind velocity (m/s)\n", " u_star : shear stress velocity (m/s)\n", " --------------------------------------------------------\n", " \n", " Return a function with w and u_star as degrees of freedom\n", " \"\"\"\n", " # get the constant values\n", " Dict_value = {z:z_val,kappa:kappa.definition.default}\n", " \n", " # compile the function\n", " VH_func = aesara_function([w,u_star],[VH.definition.expr.subs(Dict_value)], dims = {w:1, u_star:1})\n", " \n", " return(VH_func)" ] }, { "cell_type": "code", "execution_count": 15, Oscar Corvi committed Jul 15, 2021 866 "id": "shaped-object", Oscar Corvi committed Jul 15, 2021 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 "metadata": {}, "outputs": [], "source": [ "def d_func_compiled():\n", " \"\"\"Compile the zero plane displacement height function\n", " --------------------------------------------------------\n", " VH : Vegetation height\n", " --------------------------------------------------------\n", " \n", " return a function with VH as degree of freedom\n", " \"\"\"\n", " \n", " # compile the function \n", " d_func = aesara_function([VH], [d.definition.expr], dims = {VH:1})\n", " \n", " return(d_func)" ] }, { "cell_type": "code", "execution_count": 16, Oscar Corvi committed Jul 15, 2021 888 "id": "decreased-wilson", Oscar Corvi committed Jul 15, 2021 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 "metadata": {}, "outputs": [], "source": [ "def zom_func_compiled():\n", " \"\"\"Compile the characteristic momentum height exchange\n", " --------------------------------------------------------\n", " VH : Vegetation height\n", " --------------------------------------------------------\n", " \n", " return a function with VH as degree of freedom\n", " \"\"\"\n", " \n", " # compile the function \n", " zom_func = aesara_function([VH], [z_om.definition.expr], dims = {VH:1})\n", " \n", " return(zom_func)" ] }, { "cell_type": "code", "execution_count": 17, Oscar Corvi committed Jul 15, 2021 910 "id": "opponent-heritage", Oscar Corvi committed Jul 15, 2021 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 "metadata": {}, "outputs": [], "source": [ "def zoh_func_compiled():\n", " \"\"\"Compile the characteristic heat height exchange\n", " --------------------------------------------------------\n", " VH : Vegetation height\n", " --------------------------------------------------------\n", " \n", " return a function with VH as degree of freedom\n", " \"\"\"\n", " \n", " # compile the function \n", " zoh_func = aesara_function([z_om], [z_oh.definition.expr], dims = {z_om:1})\n", " \n", " return(zoh_func)" ] }, { "cell_type": "code", "execution_count": 18, Oscar Corvi committed Jul 15, 2021 932 "id": "undefined-mailing", Oscar Corvi committed Jul 15, 2021 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 "metadata": {}, "outputs": [], "source": [ "def ra_func_compiled(z_val):\n", " \"\"\"Substitutes the different terms of the r_a expression\n", " --------------------------------------------------------\n", " z : height of the measurement (m)\n", " \n", " d : zero plane displacement height (m)\n", " zoh_val : characteristic height of the heat transfert\n", " zom_val : characteristic height of the momentum transfert\n", " --------------------------------------------------------\n", " \n", " returns the compiled expression of r_a evaluable according to the wind speed\n", " \"\"\"\n", " # evaluate the values in the expression\n", " Dict_value = {z:z_val,kappa:kappa.definition.default}\n", " \n", " # compile the function\n", " ra_func = aesara_function([z_om,z_oh,d,w], [r_a.definition.expr.subs(Dict_value)], dims = {z_om:1,z_oh:1,d:1,w:1})\n", " \n", " return(ra_func)" ] }, { "cell_type": "code", "execution_count": 19, Oscar Corvi committed Jul 15, 2021 960 "id": "diverse-bulgarian", Oscar Corvi committed Jul 15, 2021 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 "metadata": {}, "outputs": [], "source": [ "def ea_func_compiled():\n", " \"\"\" Compute the actual water vapour deficit with RH and T (min/max) left as degree of freedom\n", " --------------------------------------------------------\n", " c1 : internal variable \n", " c2 : internal variable \n", " \n", " T_min : time serie of daily min temperature\n", " T_max : time serie of daily max temperature \n", " RH_min : time serie of daily min relative humidity \n", " RH_max : time serie of daily max relative humidity\n", " --------------------------------------------------------\n", " \n", " retunrs the compiled expression of the e_a function with four degrees of freedom \n", " \"\"\"\n", " \n", " # get the constants\n", " Dict_value = {c1_e:c1_e.definition.default, c2_e:c2_e.definition.default}\n", " \n", " #compile the function\n", " ea_func = aesara_function([T_min,T_max,RH_min,RH_max],[e_a.definition.expr.subs(Dict_value)], dims={T_min:1, T_max:1, RH_min:1, RH_max:1})\n", " \n", " return(ea_func)" ] }, { "cell_type": "code", "execution_count": 20, Oscar Corvi committed Jul 15, 2021 991 "id": "deadly-spice", Oscar Corvi committed Jul 15, 2021 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 "metadata": {}, "outputs": [], "source": [ "def es_func_compiled():\n", " \"\"\"Compute the saturation water vapour deficit with T (min / max) left as degree of freedom \n", " --------------------------------------------------------\n", " c1 : internal variable \n", " c2 : internal variable \n", " \n", " T_min : time serie of daily min temperature\n", " T_max : time serie of daily max temperature \n", " --------------------------------------------------------\n", " \n", " retunrs the compiled expression of the e_s function with four degrees of freedom \n", " \"\"\"\n", " \n", " # get the constants\n", " Dict_value = {c1_e:c1_e.definition.default, c2_e:c2_e.definition.default}\n", " \n", " #compile the function\n", " ea_func = aesara_function([T_min,T_max],[e_s.definition.expr.subs(Dict_value)], dims={T_min:1, T_max:1})\n", " \n", " return(ea_func) " ] }, { "cell_type": "code", "execution_count": 21, Oscar Corvi committed Jul 15, 2021 1020 "id": "pressed-familiar", Oscar Corvi committed Jul 15, 2021 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 "metadata": {}, "outputs": [], "source": [ "def PM_compiled():\n", " \"\"\" Compute the compiled version of the PM VPD equation\n", " --------------------------------------------------------\n", " c_p : specific heat of the air\n", " rho_a : mean air density\n", " gamma : psychrometric constant\n", " L : Latent heat flux\n", " \n", " r_s : Surface resistance -> given (can also be modeled)\n", " G : ground heat flux -> comes from the data\n", " Rn : net radiation flux -> comes from the data \n", " Delta : slope of the saturation curve -> computed above\n", " r_a : aerodynamic resistance -> computed above\n", " --------------------------------------------------------\n", " \n", " returns the evaporation flux (in mm/time) with Delta, G, Rn, e_a, e_s, r_a as degrees of freedom\n", " \"\"\"\n", " \n", " # get the constant values\n", " Dict_value = {c_p:c_p.definition.default, rho_a:rho_a.definition.default, L:L.definition.default, gamma:gamma.definition.default}\n", " \n", " # compile the function\n", " PM_func = aesara_function([G,Rn,Delta,VPD,g_a, g_s], [eq_PM_g.rhs.subs(Dict_value)], dims = {G:1,Rn:1,Delta:1,VPD:1,g_a:1, g_s:1})\n", " \n", " return(PM_func)" ] }, { "cell_type": "code", "execution_count": 22, Oscar Corvi committed Jul 15, 2021 1054 "id": "civilian-toner", Oscar Corvi committed Jul 15, 2021 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 "metadata": {}, "outputs": [], "source": [ "def PT_compiled():\n", " \"\"\"Compute the Priestley-Taylor equation,\n", " need 4 input : temperature, net radiations, ground heat flux and alpha PT parameter\n", " Each must be given as np.array\n", " Return the compiled function\n", " \"\"\"\n", " \n", " # creating the dictionnary with all default values from the above defined constants\n", " var_dict = Variable.__defaults__.copy()\n", " \n", " # Computing the values of evaporation using the Priestley-Taylor model\n", " PT_func = aesara_function([Delta,Rn,G, alpha_PT],[eq_PT.rhs.subs(var_dict)],dims = {Delta:1,Rn:1,G:1, alpha_PT:1})\n", "\n", " return(PT_func)" ] }, { "cell_type": "code", "execution_count": 23, Oscar Corvi committed Jul 15, 2021 1077 "id": "absent-arthritis", Oscar Corvi committed Jul 15, 2021 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 "metadata": {}, "outputs": [], "source": [ "def rs_PM_inv():\n", " \"Derive the time serie of the surface resistance out of the observed latent heat fluxes --> inverse modelling of the PM equation\"\n", " \n", " #get the constant values \n", " Dict_value = {c_p:c_p.definition.default, rho_a:rho_a.definition.default, L:L.definition.default, gamma:gamma.definition.default}\n", " \n", " # compile the function\n", " Inv_PM = aesara_function([E,G,Rn,Delta,VPD,r_a], [eq_PM_inv.rhs.subs(Dict_value)], dims = {E:1,G:1,Rn:1,Delta:1,VPD:1,r_a:1})\n", " \n", " return(Inv_PM)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 1095 "id": "breathing-manual", Oscar Corvi committed Jul 15, 2021 1096 1097 1098 1099 1100 1101 1102 1103 "metadata": {}, "source": [ "### Assign the different compiled functions to variables functions (create the functions in python)" ] }, { "cell_type": "code", "execution_count": 24, Oscar Corvi committed Jul 15, 2021 1104 "id": "robust-maker", Oscar Corvi committed Jul 15, 2021 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 "metadata": {}, "outputs": [], "source": [ "# Water_stress properties: \n", "rising_slope = rising_slope_compiled() # takes theta, theta_3, theta_4 in this order as input\n", "desc_slope = desc_slope_compiled() # takes theta, theta_1, theta_2 in this order as input\n", "\n", "# properties : \n", "delta_func = Delta_compiled() # takes Ta as input\n", "z_val = 23 # change the values of the aerodynamic constants here !!!\n", "VH_func = VH_func_compiled(z_val)\n", "d_func = d_func_compiled()\n", "zom_func = zom_func_compiled()\n", "zoh_func = zoh_func_compiled()\n", "ra_func = ra_func_compiled(z_val)\n", "eSat_func = es_func_compiled()\n", "ea_func = ea_func_compiled()\n", "\n", "# models\n", "PM_func = PM_compiled()\n", "PT_func = PT_compiled()\n", "Inv_PM_func = rs_PM_inv()" ] }, { "cell_type": "code", "execution_count": 25, Oscar Corvi committed Jul 15, 2021 1132 "id": "respected-sessions", Oscar Corvi committed Jul 15, 2021 1133 1134 1135 "metadata": {}, "outputs": [], "source": [ Oscar Corvi committed Jul 15, 2021 1136 "def stress_factor_func(psi_vec,Psi_3,Psi_4,a):\n", Oscar Corvi committed Jul 15, 2021 1137 1138 1139 1140 1141 1142 " \n", " Length = psi_vec.size\n", " \n", " Stress_func = np.zeros((Length,))\n", " Psi_3 = np.array([Psi_3])\n", " Psi_4 = np.array([Psi_4])\n", Oscar Corvi committed Jul 15, 2021 1143 " \n", Oscar Corvi committed Jul 15, 2021 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 " for j in range(Length):\n", " try:\n", " Psi_val = psi_vec[j]\n", " except Exception as error:\n", " print(psi_vec,error)\n", " # have to convert float to arrays in order to run the compiled functions\n", " Psi_val = np.array([Psi_val])\n", " if (Psi_val < Psi_4):\n", " Stress_func[j] = 0\n", " elif (Psi_val >= Psi_4) & (Psi_val < Psi_3):\n", Oscar Corvi committed Jul 15, 2021 1154 1155 1156 1157 1158 " linear = (Psi_val-Psi_4)/(Psi_3-Psi_4)\n", " if a == 0:\n", " Stress_func[j] = linear\n", " else:\n", " Stress_func[j] = (1-np.exp(a*linear))/(1-np.exp(a))\n", Oscar Corvi committed Jul 15, 2021 1159 1160 1161 1162 1163 1164 1165 " else:\n", " Stress_func[j] = 1\n", " return(Stress_func)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 1166 "id": "dense-prairie", Oscar Corvi committed Jul 15, 2021 1167 1168 1169 1170 1171 1172 1173 1174 "metadata": {}, "source": [ "## Functions to run the different models\n", "Once the functions has been defined in sympy, compiled with aesara and assign to a useful python function, it is now time to link it with the data to carry out the final computations ! All the following functions take a dataframe as input, and the related parameters ($\\theta_3$ and $\\theta_4$ for the stress function) and return a numpy array and a dictionnary containing the values of the model run and some miscellaneous information." ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 1175 "id": "valuable-isaac", Oscar Corvi committed Jul 15, 2021 1176 1177 1178 1179 1180 1181 1182 1183 "metadata": {}, "source": [ "### Varying surface resistance model" ] }, { "cell_type": "code", "execution_count": 26, Oscar Corvi committed Jul 15, 2021 1184 "id": "electric-kitty", Oscar Corvi committed Jul 15, 2021 1185 1186 1187 "metadata": {}, "outputs": [], "source": [ Oscar Corvi committed Jul 15, 2021 1188 "def PM_run_var(data, Psi_3_val, Psi_4_val,shape, gs_val = 1/70, compute_VPD = False):\n", Oscar Corvi committed Jul 15, 2021 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 " \"\"\"run varying SR Penman Monteith model but with VPD data instead of Ea and Es\n", " -----------------------------------\n", " data: list containing the data /!\\ the data should be in a specific order : Data = [Ta, Fn, Fg, Sws, Fe, Ws, Ustar, Ta_min, Ta_max, RH_min, RH_max]\n", " Psi_3_val: vector of the same size as the vectors in data, full of the value Psi_3\n", " Psi_4_val: vector of the same size as the vectors in data, full of the value Psi_4\n", " -----------------------------------\n", " \"\"\"\n", " \n", " # unpack the variables\n", " Ta_val = data[\"Ta\"].to_numpy()\n", " Fn_val = data[\"Fn\"].to_numpy()\n", " Fg_val = data[\"Fg\"].to_numpy()\n", " Sws_val = data[\"Sws\"].to_numpy()\n", " Fe_val = data[\"Fe\"].to_numpy()\n", " Ws_val = data[\"Ws\"].to_numpy()\n", " Ustar_val = data[\"ustar\"].to_numpy()\n", " VPD_val = data[\"VPD\"].to_numpy()\n", " fPAR_val = data[\"fPAR\"].to_numpy()\n", " \n", " if compute_VPD:\n", " T_min_val = data[\"Ta_min\"]\n", " T_max_val = data[\"Ta_max\"]\n", " \n", " RH_min_val = data[\"RH_min\"]\n", " RH_max_val = data[\"RH_max\"]\n", " \n", " VPD_val = eSat_func(T_min_val,T_max_val) - ea_func(T_min_val,T_max_val,RH_min_val,RH_max_val)\n", " \n", " # --------------------------\n", " # derive the two Penman models\n", " # --------------------------\n", " \n", "\n", " # Stress factor:\n", Oscar Corvi committed Jul 15, 2021 1223 " FF_vec = stress_factor_func(Sws_val,Psi_3_val,Psi_4_val, shape)\n", Oscar Corvi committed Jul 15, 2021 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 " # aerodynamic resistance:\n", " VH_T = VH_func(Ws_val,Ustar_val)\n", " displ_T = d_func(VH_T)\n", " ZOM_T = zom_func(VH_T)\n", " ZOH_T = zoh_func(ZOM_T)\n", " Ra_T = ra_func(ZOM_T, ZOH_T, displ_T, Ws_val)\n", " Ga_T = 1/Ra_T\n", "\n", " # surface resistance:\n", " Gs_T = gs_val*FF_vec+0.0001\n", " # thermodynamic parameters\n", " D_T = delta_func(Ta_val)\n", "\n", " # compile the Ea values :\n", " PM_var = fPAR_val*PM_func(Fg_val,Fn_val,D_T,VPD_val,Ga_T, Gs_T) # R_s varying with theta\n", " \n", " Dic_var = {\"ga\":Ga_T, \"gs\":Gs_T, \"D_T\":D_T}\n", " \n", " return(PM_var)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 1247 "id": "featured-trial", Oscar Corvi committed Jul 15, 2021 1248 1249 1250 1251 1252 1253 1254 1255 "metadata": {}, "source": [ "### Constant surface conductance model" ] }, { "cell_type": "code", "execution_count": 27, Oscar Corvi committed Jul 15, 2021 1256 "id": "systematic-calibration", Oscar Corvi committed Jul 15, 2021 1257 1258 1259 "metadata": {}, "outputs": [], "source": [ Oscar Corvi committed Jul 15, 2021 1260 "def PM_run_cst(data, Psi_3_val, Psi_4_val,shape, gs_val = 1/70, compute_VPD = False):\n", Oscar Corvi committed Jul 15, 2021 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 " \"\"\"run constant SR Penman Monteith mode but with VPD data instead of Ea and Es\n", " -----------------------------------\n", " data: list containing the data /!\\ the data should be in a specific order : Data = [Ta, Fn, Fg, Sws, Fe, Ws, Ustar, Ta_min, Ta_max, RH_min, RH_max]\n", " T1_val: vector of the same size as the vectors in data, full of the value T1\n", " T3_val: vector of the same size as the vectors in data, full of the value T3\n", " -----------------------------------\n", " \"\"\"\n", " \n", " # unpack the variables\n", " Ta_val = data[\"Ta\"].to_numpy()\n", " Fn_val = data[\"Fn\"].to_numpy()\n", " Fg_val = data[\"Fg\"].to_numpy()\n", " Sws_val = data[\"Sws\"].to_numpy()\n", " Fe_val = data[\"Fe\"].to_numpy()\n", " Ws_val = data[\"Ws\"].to_numpy()\n", " Ustar_val = data[\"ustar\"].to_numpy()\n", " VPD_val = data[\"VPD\"].to_numpy()\n", " fPAR_val = data[\"fPAR\"].to_numpy()\n", " \n", " if compute_VPD:\n", " T_min_val = data[\"Ta_min\"]\n", " T_max_val = data[\"Ta_max\"]\n", " \n", " RH_min_val = data[\"RH_min\"]\n", " RH_max_val = data[\"RH_max\"]\n", " \n", " VPD_val = eSat_func(T_min_val,T_max_val) - ea_func(T_min_val,T_max_val,RH_min_val,RH_max_val)\n", " \n", " # --------------------------\n", " # derive the two Penman models\n", " # --------------------------\n", " \n", "\n", " # Stress factor:\n", Oscar Corvi committed Jul 15, 2021 1295 " FF_vec = stress_factor_func(Sws_val,Psi_3_val,Psi_4_val,shape)\n", Oscar Corvi committed Jul 15, 2021 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 " \n", " # aerodynamic resistance:\n", " VH_T = VH_func(Ws_val,Ustar_val)\n", " displ_T = d_func(VH_T)\n", " ZOM_T = zom_func(VH_T)\n", " ZOH_T = zoh_func(ZOM_T)\n", " Ra_T = ra_func(ZOM_T, ZOH_T, displ_T, Ws_val)\n", " Ga_T = 1/Ra_T\n", "\n", " # surface resistance:\n", " Gs_C = gs_val*np.ones((Ta_val.size,)) # -> for constant resistance model -> Rs is constant and Ea = S(theta)*E_PM\n", " # thermodynamic parameters\n", " D_T = delta_func(Ta_val)\n", "\n", " # compile the Ea values :\n", " PM_cst = fPAR_val*FF_vec*PM_func(Fg_val,Fn_val,D_T,VPD_val,Ga_T, Gs_C) # R_s constant but stress factor in front of the PM evaluation\n", " \n", " Dic_var = {\"ga\":Ga_T, \"gs\":Gs_C, \"D_T\":D_T}\n", " \n", " return(PM_cst)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 1320 "id": "together-repository", Oscar Corvi committed Jul 15, 2021 1321 1322 1323 1324 1325 1326 1327 1328 "metadata": {}, "source": [ "### Benchmark Penman-Monteith model" ] }, { "cell_type": "code", "execution_count": 28, Oscar Corvi committed Jul 15, 2021 1329 "id": "worse-launch", Oscar Corvi committed Jul 15, 2021 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 "metadata": {}, "outputs": [], "source": [ "def PM_run_classic(data, gs_val = 1/70, compute_VPD = False):\n", " \"\"\"run classic PM model (only Rs as calibration parameter)\n", " -----------------------------------\n", " data: list containing the data /!\\ the data should be in a specific order : Data = [Ta, Fn, Fg, Sws, Fe, Ws, Ustar, Ta_min, Ta_max, RH_min, RH_max]\n", " Rs_val: value of the SR\n", " -----------------------------------\n", " \"\"\"\n", " \n", " # unpack the variables\n", " Ta_val = data[\"Ta\"].to_numpy()\n", " Fn_val = data[\"Fn\"].to_numpy()\n", " Fg_val = data[\"Fg\"].to_numpy()\n", " Sws_val = data[\"Sws\"].to_numpy()\n", " Fe_val = data[\"Fe\"].to_numpy()\n", " Ws_val = data[\"Ws\"].to_numpy()\n", " Ustar_val = data[\"ustar\"].to_numpy()\n", " VPD_val = data[\"VPD\"].to_numpy()\n", " fPAR_val = data[\"fPAR\"].to_numpy()\n", " \n", " if compute_VPD:\n", " T_min_val = data[\"Ta_min\"]\n", " T_max_val = data[\"Ta_max\"]\n", " \n", " RH_min_val = data[\"RH_min\"]\n", " RH_max_val = data[\"RH_max\"]\n", " \n", " VPD_val = eSat_func(T_min_val,T_max_val) - ea_func(T_min_val,T_max_val,RH_min_val,RH_max_val)\n", " \n", " # --------------------------\n", " # derive the two Penman models\n", " # --------------------------\n", " \n", " # aerodynamic resistance:\n", " VH_T = VH_func(Ws_val,Ustar_val)\n", " displ_T = d_func(VH_T)\n", " ZOM_T = zom_func(VH_T)\n", " ZOH_T = zoh_func(ZOM_T)\n", " Ra_T = ra_func(ZOM_T, ZOH_T, displ_T, Ws_val)\n", " Ga_T = 1/Ra_T\n", "\n", " # surface resistance:\n", " Gs_C = gs_val*np.ones((Ta_val.size,)) # -> for constant resistance model -> Rs is constant and Ea = S(theta)*E_PM\n", " # thermodynamic parameters\n", " D_T = delta_func(Ta_val)\n", "\n", " # compile the Ea values :\n", " PM_cst = fPAR_val*PM_func(Fg_val,Fn_val,D_T,VPD_val,Ga_T, Gs_C) # R_s constant but stress factor in front of the PM evaluation\n", " \n", " Dic_var = {\"ga\":Ga_T, \"gs\":Gs_C, \"D_T\":D_T}\n", " \n", " return(PM_cst)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 1388 "id": "closing-rally", Oscar Corvi committed Jul 15, 2021 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 "metadata": {}, "source": [ "### Modified version of the PM equation\n", "\n", "2 Sided PM evapotranspiration model from *Schymanski and Or, 2017* : \n", "\\n", "E = \\frac{1}{\\lambda}\\frac{\\Delta (R_n - G) + c_p \\rho_a g_a a_{sh} VPD }{\\Delta + \\gamma \\left( 1+ \\frac{g_a}{g_s} \\right) \\frac{a_{sh}}{a_s}}\n", "\\n", "\n", "with $a_{sh}$ and $a_s$ the fraction of projected area exchanging sensible heat flux with the air and fractio of one sided-leaf area covered by stomatas respectively. In the case of amphistomateous leaves, $a_s = 2$ and $a_s = 1$ for hypostomateous leaves. For the Howard Spring site, we consider $a_s = 2$" ] }, { "cell_type": "code", "execution_count": 29, Oscar Corvi committed Jul 15, 2021 1404 "id": "rational-improvement", Oscar Corvi committed Jul 15, 2021 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 "metadata": {}, "outputs": [], "source": [ "def PM_run_2var(data, Psi_3_val, Psi_4_val, gs_val = 1/70, compute_VPD = False):\n", " \"\"\"run varying SR Penman Monteith model but with VPD data instead of Ea and Es\n", " -----------------------------------\n", " data: list containing the data /!\\ the data should be in a specific order : Data = [Ta, Fn, Fg, Sws, Fe, Ws, Ustar, Ta_min, Ta_max, RH_min, RH_max]\n", " Psi_3_val: vector of the same size as the vectors in data, full of the value Psi_3\n", " Psi_4_val: vector of the same size as the vectors in data, full of the value Psi_4\n", " -----------------------------------\n", " \"\"\"\n", " \n", " # unpack the variables\n", " Ta_val = data[\"Ta\"].to_numpy()\n", " Fn_val = data[\"Fn\"].to_numpy()\n", " Fg_val = data[\"Fg\"].to_numpy()\n", " Sws_val = data[\"Sws\"].to_numpy()\n", " Fe_val = data[\"Fe\"].to_numpy()\n", " Ws_val = data[\"Ws\"].to_numpy()\n", " Ustar_val = data[\"ustar\"].to_numpy()\n", " VPD_val = data[\"VPD\"].to_numpy()\n", " fPAR_val = data[\"fPAR\"].to_numpy()\n", " \n", " if compute_VPD:\n", " T_min_val = data[\"Ta_min\"]\n", " T_max_val = data[\"Ta_max\"]\n", " \n", " RH_min_val = data[\"RH_min\"]\n", " RH_max_val = data[\"RH_max\"]\n", " \n", " VPD_val = eSat_func(T_min_val,T_max_val) - ea_func(T_min_val,T_max_val,RH_min_val,RH_max_val)\n", " \n", " # --------------------------\n", " # derive the two Penman models\n", " # --------------------------\n", " \n", "\n", " # Stress factor:\n", " FF_vec = stress_factor_func(Sws_val,Psi_3_val,Psi_4_val)\n", " # aerodynamic resistance:\n", " VH_T = VH_func(Ws_val,Ustar_val)\n", " displ_T = d_func(VH_T)\n", " ZOM_T = zom_func(VH_T)\n", " ZOH_T = zoh_func(ZOM_T)\n", " Ra_T = ra_func(ZOM_T, ZOH_T, displ_T, Ws_val)\n", " Ga_T = 2/Ra_T # multiply by 2 to account for the 2 sided exchange of latent heat flux\n", "\n", " # surface resistance:\n", " Gs_T = gs_val*FF_vec+0.0001\n", " # thermodynamic parameters\n", " D_T = delta_func(Ta_val)\n", "\n", " # compile the Ea values :\n", " PM_var = fPAR_val*PM_func(Fg_val,Fn_val,D_T,VPD_val,Ga_T, Gs_T) # R_s varying with theta\n", " \n", " Dic_var = {\"ga\":Ga_T, \"gs\":Gs_T, \"D_T\":D_T}\n", " \n", " return(PM_var)" ] }, { "cell_type": "code", "execution_count": 30, Oscar Corvi committed Jul 15, 2021 1468 "id": "owned-degree", Oscar Corvi committed Jul 15, 2021 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 "metadata": {}, "outputs": [], "source": [ "def PM_run_2cst(data, Psi_3_val, Psi_4_val, gs_val = 1/70, compute_VPD = False):\n", " \"\"\"run constant SR Penman Monteith mode but with VPD data instead of Ea and Es\n", " -----------------------------------\n", " data: list containing the data /!\\ the data should be in a specific order : Data = [Ta, Fn, Fg, Sws, Fe, Ws, Ustar, Ta_min, Ta_max, RH_min, RH_max]\n", " T1_val: vector of the same size as the vectors in data, full of the value T1\n", " T3_val: vector of the same size as the vectors in data, full of the value T3\n", " -----------------------------------\n", " \"\"\"\n", " \n", " # unpack the variables\n", " Ta_val = data[\"Ta\"].to_numpy()\n", " Fn_val = data[\"Fn\"].to_numpy()\n", " Fg_val = data[\"Fg\"].to_numpy()\n", " Sws_val = data[\"Sws\"].to_numpy()\n", " Fe_val = data[\"Fe\"].to_numpy()\n", " Ws_val = data[\"Ws\"].to_numpy()\n", " Ustar_val = data[\"ustar\"].to_numpy()\n", " VPD_val = data[\"VPD\"].to_numpy()\n", " fPAR_val = data[\"fPAR\"].to_numpy()\n", " \n", " if compute_VPD:\n", " T_min_val = data[\"Ta_min\"]\n", " T_max_val = data[\"Ta_max\"]\n", " \n", " RH_min_val = data[\"RH_min\"]\n", " RH_max_val = data[\"RH_max\"]\n", " \n", " VPD_val = eSat_func(T_min_val,T_max_val) - ea_func(T_min_val,T_max_val,RH_min_val,RH_max_val)\n", " \n", " # --------------------------\n", " # derive the two Penman models\n", " # --------------------------\n", " \n", "\n", " # Stress factor:\n", " FF_vec = stress_factor_func(Sws_val,Psi_3_val,Psi_4_val)\n", " \n", " # aerodynamic resistance:\n", " VH_T = VH_func(Ws_val,Ustar_val)\n", " displ_T = d_func(VH_T)\n", " ZOM_T = zom_func(VH_T)\n", " ZOH_T = zoh_func(ZOM_T)\n", " Ra_T = ra_func(ZOM_T, ZOH_T, displ_T, Ws_val)\n", " Ga_T = 2/Ra_T # multiply by 2 to account for the 2 sided exchange of latent heat flux\n", "\n", " # surface resistance:\n", " Gs_C = gs_val*np.ones((Ta_val.size,)) # -> for constant resistance model -> Rs is constant and Ea = S(theta)*E_PM\n", " # thermodynamic parameters\n", " D_T = delta_func(Ta_val)\n", "\n", " # compile the Ea values :\n", " PM_cst = fPAR_val*FF_vec*PM_func(Fg_val,Fn_val,D_T,VPD_val,Ga_T, Gs_C) # R_s constant but stress factor in front of the PM evaluation\n", " \n", " Dic_var = {\"ga\":Ga_T, \"gs\":Gs_C, \"D_T\":D_T}\n", " \n", " return(PM_cst)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 1532 "id": "helpful-painting", Oscar Corvi committed Jul 15, 2021 1533 1534 1535 1536 1537 1538 1539 "metadata": {}, "source": [ "### Priestley and Taylor model" ] }, { "cell_type": "code", Oscar Corvi committed Jul 15, 2021 1540 "execution_count": 71, Oscar Corvi committed Jul 15, 2021 1541 "id": "applicable-dominant", Oscar Corvi committed Jul 15, 2021 1542 1543 1544 "metadata": {}, "outputs": [], "source": [ Oscar Corvi committed Jul 15, 2021 1545 "def PT_run(data,Psi_3_val, Psi_4_val, shape, alpha_val = 1.26, compute_VPD = False):\n", Oscar Corvi committed Jul 15, 2021 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 " \"\"\"run classic PM model (only Rs as calibration parameter)\n", " -----------------------------------\n", " data: list containing the data /!\\ the data should be in a specific order : Data = [Ta, Fn, Fg, Sws, Fe, Ws, Ustar, Ta_min, Ta_max, RH_min, RH_max]\n", " Rs_val: value of the SR\n", " -----------------------------------\n", " \"\"\"\n", " \n", " # unpack the variables\n", " Ta_val = data[\"Ta\"].to_numpy()\n", " Fn_val = data[\"Fn\"].to_numpy()\n", " Fg_val = data[\"Fg\"].to_numpy()\n", " Sws_val = data[\"Sws\"].to_numpy()\n", " #Fe_val = data[\"Fe\"].to_numpy()\n", " #Ws_val = data[\"Ws\"].to_numpy()\n", " #Ustar_val = data[\"ustar\"].to_numpy()\n", " VPD_val = data[\"VPD\"].to_numpy()\n", " fPAR_val = data[\"fPAR\"].to_numpy()\n", " \n", " if compute_VPD:\n", " T_min_val = data[\"Ta_min\"]\n", " T_max_val = data[\"Ta_max\"]\n", " \n", " RH_min_val = data[\"RH_min\"]\n", " RH_max_val = data[\"RH_max\"]\n", " \n", " VPD_val = eSat_func(T_min_val,T_max_val) - ea_func(T_min_val,T_max_val,RH_min_val,RH_max_val)\n", " \n", " # --------------------------\n", " # derive the two Penman models\n", " # --------------------------\n", "\n", " # Stress factor:\n", Oscar Corvi committed Jul 15, 2021 1578 " FF_vec = stress_factor_func(Sws_val,Psi_3_val,Psi_4_val, shape)\n", Oscar Corvi committed Jul 15, 2021 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 " \n", " # surface resistance:\n", " Alpha_vec = alpha_val*np.ones((Ta_val.size,))\n", "\n", " # thermodynamic parameters\n", " D_T = delta_func(Ta_val)\n", "\n", " # compile the Ea values :\n", " PT_mod = fPAR_val*FF_vec*PT_func(D_T,Fn_val,Fg_val,Alpha_vec)\n", " \n", " Dic_var = {\"D_T\":D_T}\n", " \n", " return(PT_mod)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 1596 "id": "sticky-necessity", Oscar Corvi committed Jul 15, 2021 1597 1598 1599 1600 1601 1602 1603 1604 1605 "metadata": {}, "source": [ "### Inverse modelling\n", "Compute the original $g_s$ time serie out of the data" ] }, { "cell_type": "code", "execution_count": 32, Oscar Corvi committed Jul 15, 2021 1606 "id": "compressed-calgary", Oscar Corvi committed Jul 15, 2021 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 "metadata": {}, "outputs": [], "source": [ "def inv_PM_run(data, compute_VPD = False):\n", " \"\"\"inverse modelling of the PM equation to derive time varying surface resistance\n", " -----------------------------------\n", " data: list containing the data /!\\ the data should be in a specific order : Data = [Ta, Fn, Fg, Sws, Fe, Ws, Ustar, Ta_min, Ta_max, RH_min, RH_max]\n", " Rs_val: value of the SR\n", " -----------------------------------\n", " \"\"\"\n", " \n", " # unpack the variables\n", " Ta_val = data[\"Ta\"].to_numpy()\n", " Fn_val = data[\"Fn\"].to_numpy()\n", " Fg_val = data[\"Fg\"].to_numpy()\n", " Sws_val = data[\"Sws\"].to_numpy()\n", " Fe_val = data[\"Fe\"].to_numpy()\n", " Ws_val = data[\"Ws\"].to_numpy()\n", " Ustar_val = data[\"ustar\"].to_numpy()\n", " VPD_val = data[\"VPD\"].to_numpy()\n", " \n", " if compute_VPD:\n", " T_min_val = data[\"Ta_min\"]\n", " T_max_val = data[\"Ta_max\"]\n", " \n", " RH_min_val = data[\"RH_min\"]\n", " RH_max_val = data[\"RH_max\"]\n", " \n", " VPD_val = eSat_func(T_min_val,T_max_val) - ea_func(T_min_val,T_max_val,RH_min_val,RH_max_val)\n", " \n", " # --------------------------\n", " # derive the two Penman models\n", " # --------------------------\n", " \n", " # aerodynamic resistance:\n", " VH_T = VH_func(Ws_val,Ustar_val)\n", " displ_T = d_func(VH_T)\n", " ZOM_T = zom_func(VH_T)\n", " ZOH_T = zoh_func(ZOM_T)\n", " Ra_T = ra_func(ZOM_T, ZOH_T, displ_T, Ws_val)\n", "\n", " # thermodynamic parameters\n", " D_T = delta_func(Ta_val)\n", "\n", " # compile the Ea values :\n", " Gs_val = 1/Inv_PM_func(Fe_val,Fg_val,Fn_val,D_T,VPD_val,Ra_T) # R_s constant but stress factor in front of the PM evaluation\n", " \n", " \n", " return(Gs_val)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 1660 "id": "intensive-return", Oscar Corvi committed Jul 15, 2021 1661 1662 1663 1664 1665 1666 "metadata": {}, "source": [ "## Calibration algorithm" ] }, { Oscar Corvi committed Jul 15, 2021 1667 "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 1668 "id": "alternative-intranet", Oscar Corvi committed Jul 15, 2021 1669 1670 "metadata": {}, "source": [ Oscar Corvi committed Jul 15, 2021 1671 1672 1673 1674 "Use the global optimizer from the scipy.optimize package. Minimize the squared residual :\n", "\\n", "\\Theta_{opt} = \\underset{\\theta_3, \\theta_4, g_s}{min} \\left( E_p(\\textbf{X}, \\theta_3, \\theta_4, g_s) - E_{obs})^2\\right)\n", "\" Oscar Corvi committed Jul 15, 2021 1675 1676 1677 1678 ] }, { "cell_type": "code", Oscar Corvi committed Jul 15, 2021 1679 "execution_count": 33, Oscar Corvi committed Jul 15, 2021 1680 "id": "still-metadata", Oscar Corvi committed Jul 15, 2021 1681 "metadata": {}, Oscar Corvi committed Jul 15, 2021 1682 1683 "outputs": [], "source": [ Oscar Corvi committed Jul 15, 2021 1684 "# def calibration(Data,model_run,bounds_shape, bounds = [(0.1,1),(0.001,0.1)], compute_VPD = False, linear = False):\n", Oscar Corvi committed Jul 15, 2021 1685 " \n", Oscar Corvi committed Jul 15, 2021 1686 1687 "# if not linear:\n", "# bounds.append(bounds_shape)\n", Oscar Corvi committed Jul 15, 2021 1688 " \n", Oscar Corvi committed Jul 15, 2021 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 "# if compute_VPD:\n", "# def residual(Coeff):\n", "# return((model_run(Data, Coeff[0], Coeff[1],Coeff[2], compute_VPD = True)-Data[\"Fe\"])**2).sum()\n", "# else:\n", "# def residual(Coeff):\n", "# return((model_run(Data, Coeff[0], Coeff[1],Coeff[2])-Data[\"Fe\"])**2).sum()\n", "# else : \n", "# if compute_VPD:\n", "# def residual(Coeff):\n", "# return((model_run(Data, Coeff[0], Coeff[1],0, compute_VPD = True)-Data[\"Fe\"])**2).sum()\n", "# else:\n", "# def residual(Coeff):\n", "# return((model_run(Data, Coeff[0], Coeff[1],0)-Data[\"Fe\"])**2).sum()\n", " \n", "# coeff_opti = optimize.shgo(residual, bounds).x\n", "# return(coeff_opti)" Oscar Corvi committed Jul 15, 2021 1705 1706 1707 1708 ] }, { "cell_type": "code", Oscar Corvi committed Jul 15, 2021 1709 "execution_count": 34, Oscar Corvi committed Jul 15, 2021 1710 "id": "floppy-rates", Oscar Corvi committed Jul 15, 2021 1711 1712 1713 "metadata": {}, "outputs": [], "source": [ Oscar Corvi committed Jul 15, 2021 1714 1715 "def calibration(Data,model_run, bounds = [(0.1,1),(0.001,0.1),(-50,50)], compute_VPD = False):\n", " \n", Oscar Corvi committed Jul 15, 2021 1716 1717 " if compute_VPD:\n", " def residual(Coeff):\n", Oscar Corvi committed Jul 15, 2021 1718 " return((model_run(Data, Coeff[0], Coeff[1],Coeff[2], compute_VPD = True)-Data[\"Fe\"])**2).sum()\n", Oscar Corvi committed Jul 15, 2021 1719 1720 " else:\n", " def residual(Coeff):\n", Oscar Corvi committed Jul 15, 2021 1721 1722 " return((model_run(Data, Coeff[0], Coeff[1],Coeff[2])-Data[\"Fe\"])**2).sum()\n", " \n", Oscar Corvi committed Jul 15, 2021 1723 1724 1725 1726 1727 1728 " coeff_opti = optimize.shgo(residual, bounds).x\n", " return(coeff_opti)" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 1729 "id": "sophisticated-canada", Oscar Corvi committed Jul 15, 2021 1730 1731 1732 1733 1734 1735 1736 "metadata": {}, "source": [ "# Part III - Experiments" ] }, { "cell_type": "markdown", Oscar Corvi committed Jul 15, 2021 1737 "id": "straight-springfield", Oscar Corvi committed Jul 15, 2021 1738 1739 1740 1741 1742 1743 1744 1745 "metadata": {}, "source": [ "## One site, one year\n", "Data from Howard Springs for the sole year 2016" ] }, { "cell_type": "code", Oscar Corvi committed Jul 15, 2021 1746 "execution_count": 35, Oscar Corvi committed Jul 15, 2021 1747 "id": "enclosed-client", Oscar Corvi committed Jul 15, 2021 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136 "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "
<xarray.Dataset>\n",        "Dimensions:                (latitude: 1, longitude: 1, time: 315551)\n",        "Coordinates:\n",        "  * time                   (time) datetime64[ns] 2002-01-01T00:30:00 ... 2019...\n",        "  * latitude               (latitude) float64 -12.5\n",        "  * longitude              (longitude) float64 131.2\n",        "Data variables: (12/143)\n",        "    Ah                     (time, latitude, longitude) float64 dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>\n",        "    Ah_QCFlag              (time, latitude, longitude) float64 dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>\n",        "    Ah_HMP_23m             (time, latitude, longitude) float64 dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>\n",        "    Ah_HMP_23m_QCFlag      (time, latitude, longitude) float64 dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>\n",        "    Ah_HMP_2m              (time, latitude, longitude) float64 dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>\n",        "    Ah_HMP_2m_QCFlag       (time, latitude, longitude) float64 dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>\n",        "    ...                     ...\n",        "    Ws_SONIC_Av_QCFlag     (time, latitude, longitude) float64 dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>\n",        "    ps                     (time, latitude, longitude) float64 dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>\n",        "    ps_QCFlag              (time, latitude, longitude) float64 dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>\n",        "    ustar                  (time, latitude, longitude) float64 dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>\n",        "    ustar_QCFlag           (time, latitude, longitude) float64 dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>\n",        "    crs                    float64 -2.147e+09\n",        "Attributes: (12/50)\n",        "    BulkDensity:              1500\n",        "    FgDepth:                  0.08\n",        "    OrganicContent:           0.01\n",        "    PythonVersion:            2.7.16 |Anaconda, Inc.| (default, Mar 14 2019, ...\n",        "    QC_version:               PyFluxPro V1.0.1\n",        "    SwsDefault:               0.10\n",        "    ...                       ...\n",        "    title:                    Flux tower data set from the Howard Springs sit...\n",        "    tower_height:             23m\n",        "    vegetation:               Woody savanna\n",        "    xl_datemode:              0\n",        "    xl_filename:              E:/My Dropbox/Dropbox/Data_flux_data/Site data ...\n",
Oscar Corvi committed Jul 15, 2021  2137                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          "    xl_moddatetime:           2020-01-21 11:59:06
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Array Chunk
Bytes 2.41 MiB 2.41 MiB
Shape (315551, 1, 1) (315551, 1, 1)
Count 4 Tasks 1 Chunks
Type float64 numpy.ndarray
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• Ah_QCFlag
(time, latitude, longitude)
float64
dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>
long_name :
AhQC flag
units :
none
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• \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Array Chunk
Bytes 2.41 MiB 2.41 MiB
Shape (315551, 1, 1) (315551, 1, 1)
Count 5 Tasks 1 Chunks
Type float64 numpy.ndarray
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• Ah_HMP_23m
(time, latitude, longitude)
float64
dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>
coverage_L3 :
73
coverage_L4 :
73
group_name :
height :
23m
instrument :
HMP45C
long_name :
Absolute humidity
serial_number :
standard_name :
not defined
units :
g/m3
valid_range :
5,30
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• \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Array Chunk
Bytes 2.41 MiB 2.41 MiB
Shape (315551, 1, 1) (315551, 1, 1)
Count 4 Tasks 1 Chunks
Type float64 numpy.ndarray
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• Ah_HMP_23m_QCFlag
(time, latitude, longitude)
float64
dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>
long_name :
Ah_HMP_23mQC flag
units :
none
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• \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Array Chunk
Bytes 2.41 MiB 2.41 MiB
Shape (315551, 1, 1) (315551, 1, 1)
Count 5 Tasks 1 Chunks
Type float64 numpy.ndarray
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• Ah_HMP_2m
(time, latitude, longitude)
float64
dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>
coverage_L3 :
66
coverage_L4 :
66
group_name :
height :
2m
instrument :
HMP45C
long_name :
Absolute humidity
serial_number :
standard_name :
not defined
units :
g/m3
valid_range :
2,30
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• \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Array Chunk
Bytes 2.41 MiB 2.41 MiB
Shape (315551, 1, 1) (315551, 1, 1)
Count 4 Tasks 1 Chunks
Type float64 numpy.ndarray
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• Ah_HMP_2m_QCFlag
(time, latitude, longitude)
float64
dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>
long_name :
Ah_HMP_2mQC flag
units :
none
\n", Oscar Corvi committed Jul 15, 2021 2431 2432 2433 2434 2435 2436 2437 2438 2439 2440 2441 2442 2443 2444 2445 2446 2447 2448 2449 2450 2451 2452 2453 2454 2455 2456 2457 2458 2459 2460 2461 2462 2463 2464 2465 2466 2467 2468 2469 2470 2471 2472 2473 2474 2475 2476 2477 2478 2479 2480 2481 2482 2483 2484 2485 2486 2487 "
• \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Array Chunk
Bytes 2.41 MiB 2.41 MiB
Shape (315551, 1, 1) (315551, 1, 1)
Count 5 Tasks 1 Chunks
Type float64 numpy.ndarray
\n", "
\n", "\n", "
\n", "\n", "\n", "\n", Oscar Corvi committed Jul 15, 2021 2488 "
• Ah_IRGA_Av
(time, latitude, longitude)
float64
dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>
coverage_L3 :
76
coverage_L4 :
76
group_name :
height :
23m
instrument :
Li-7500
long_name :
Absolute humidity
serial_number :
standard_name :
not defined
units :
g/m3
valid_range :
2,35
\n", Oscar Corvi committed Jul 15, 2021 2489 2490 2491 2492 2493 2494 2495 2496 2497 2498 2499 2500 2501 2502 2503 2504 2505 2506 2507 2508 2509 2510 2511 2512 2513 2514 2515 2516 2517 2518 2519 2520 2521 2522 2523 2524 2525 2526 2527 2528 2529 2530 2531 2532 2533 2534 2535 2536 2537 2538 2539 2540 2541 2542 2543 2544 2545 "
• \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Array Chunk
Bytes 2.41 MiB 2.41 MiB
Shape (315551, 1, 1) (315551, 1, 1)
Count 4 Tasks 1 Chunks
Type float64 numpy.ndarray
\n", "
\n", "\n", "
\n", "\n", "\n", "\n", Oscar Corvi committed Jul 15, 2021 2546 "
• Ah_IRGA_Av_QCFlag
(time, latitude, longitude)
float64
dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>
long_name :
Ah_IRGA_AvQC flag
units :
none
\n", Oscar Corvi committed Jul 15, 2021 2547 2548 2549 2550 2551 2552 2553 2554 2555 2556 2557 2558 2559 2560 2561 2562 2563 2564 2565 2566 2567 2568 2569 2570 2571 2572 2573 2574 2575 2576 2577 2578 2579 2580 2581 2582 2583 2584 2585 2586 2587 2588 2589 2590 2591 2592 2593 2594 2595 2596 2597 2598 2599 2600 2601 2602 2603 "
• \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Array Chunk
Bytes 2.41 MiB 2.41 MiB
Shape (315551, 1, 1) (315551, 1, 1)
Count 5 Tasks 1 Chunks
Type float64 numpy.ndarray
\n", "
\n", "\n", "
\n", "\n", "\n", "\n", Oscar Corvi committed Jul 15, 2021 2604 "
• Ah_IRGA_Sd
(time, latitude, longitude)
float64
dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>
coverage_L3 :
84
coverage_L4 :
84
group_name :
height :
not defined
instrument :
not defined
long_name :
Absolute humidity
serial_number :
not defined
standard_name :
not defined
units :
g/m3
valid_range :
0,20
\n", Oscar Corvi committed Jul 15, 2021 2605 2606 2607 2608 2609 2610 2611 2612 2613 2614 2615 2616 2617 2618 2619 2620 2621 2622 2623 2624 2625 2626 2627 2628 2629 2630 2631 2632 2633 2634 2635 2636 2637 2638 2639 2640 2641 2642 2643 2644 2645 2646 2647 2648 2649 2650 2651 2652 2653 2654 2655 2656 2657 2658 2659 2660 2661 "
• \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Array Chunk
Bytes 2.41 MiB 2.41 MiB
Shape (315551, 1, 1) (315551, 1, 1)
Count 4 Tasks 1 Chunks
Type float64 numpy.ndarray
\n", "
\n", "\n", "
\n", "\n", "\n", "\n", Oscar Corvi committed Jul 15, 2021 2662 "
• Ah_IRGA_Sd_QCFlag
(time, latitude, longitude)
float64
dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>
long_name :
Ah_IRGA_SdQC flag
units :
none
\n", Oscar Corvi committed Jul 15, 2021 2663 2664 2665 2666 2667 2668 2669 2670 2671 2672 2673 2674 2675 2676 2677 2678 2679 2680 2681 2682 2683 2684 2685 2686 2687 2688 2689 2690 2691 2692 2693 2694 2695 2696 2697 2698 2699 2700 2701 2702 2703 2704 2705 2706 2707 2708 2709 2710 2711 2712 2713 2714 2715 2716 2717 2718 2719 "
• \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Array Chunk
Bytes 2.41 MiB 2.41 MiB
Shape (315551, 1, 1) (315551, 1, 1)
Count 5 Tasks 1 Chunks
Type float64 numpy.ndarray
\n", "
\n", "\n", "
\n", "\n", "\n", "\n", Oscar Corvi committed Jul 15, 2021 2720 "
• Ah_IRGA_Vr
(time, latitude, longitude)
float64
dask.array<chunksize=(315551, 1, 1), meta=np.ndarray>
coverage_L3 :
82
coverage_L4 :
82
group_name :
height :
23m
instrument :
Li-7500
long_name :
Absolute humidity
serial_number :
standard_name :
not defined
units :
(g/m3)2
valid_range :
0,400
\n", Oscar Corvi committed Jul 15, 2021 2721 2722 2723 2724 2725 2726 2727 2728 2729 2730 2731 2732 2733 2734 2735 2736 2737 2738 2739 2740 2741 2742 2743 2744 2745 2746 2747 2748 2749 2750 2751 2752 2753 2754 2755 2756 2757