├── results ├── eGRF_TPL_2D │ ├── angles.txt │ ├── diff.pdf │ ├── 0000_diff.pdf │ ├── 0001_diff.pdf │ ├── 0002_diff.pdf │ ├── 0003_diff.pdf │ ├── 0004_diff.pdf │ ├── 0005_diff.pdf │ ├── 0006_diff.pdf │ ├── 0007_diff.pdf │ ├── para0000 │ │ └── para.txt │ ├── para0001 │ │ └── para.txt │ ├── para0002 │ │ └── para.txt │ ├── para0003 │ │ └── para.txt │ ├── para0004 │ │ ├── para.txt │ │ └── rad_mean_head.txt │ ├── para0005 │ │ ├── para.txt │ │ └── rad_mean_head.txt │ ├── para0006 │ │ └── para.txt │ ├── para0007 │ │ └── para.txt │ ├── time.txt │ └── rad.txt ├── 05_KTPL.pdf ├── 04_trans_plot.pdf ├── 09_tpl_family.pdf ├── 02_step_functions.pdf ├── 06_matern_tpl_1-5.pdf ├── 07_matern_tpl_0-5.pdf ├── 08_matern_family.pdf ├── 00_ext_theis_tpl_2D.pdf ├── 10_field_matern_1-5.pdf ├── 11_field_matern_0-5.pdf ├── 01_ext_theis_tpl_conv.pdf └── 03_literature_comparison.pdf ├── requirements.txt ├── src ├── comparison │ ├── 00_run_sim_mpi.sh │ ├── 02_compare_mean.py │ └── 01_run_sim.py ├── 01_convergence.py ├── 00_ext_theis_tpl.py ├── 04_trans_plot.py ├── 02_step_function.py ├── 05_KTPL_plot.py ├── 06_tplgaussian_vs_matern.py └── 03_literature_transmissivities.py ├── .zenodo.json ├── LICENSE ├── .gitignore └── README.md /results/eGRF_TPL_2D/angles.txt: -------------------------------------------------------------------------------- 1 | 6.400000000000000000e+01 2 | -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | gstools==1.3.0 2 | anaflow==1.0.1 3 | ogs5py==1.1.1 4 | matplotlib 5 | -------------------------------------------------------------------------------- /src/comparison/00_run_sim_mpi.sh: -------------------------------------------------------------------------------- 1 | #!/bin/bash 2 | 3 | mpiexec -n 4 python3 01_run_sim.py 4 | -------------------------------------------------------------------------------- /results/05_KTPL.pdf: 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1.000000000000000048e-04 3 | 1.000000000000000048e-04 4 | 1.000000000000000000e+00 5 | 1.000000000000000000e+01 6 | 5.000000000000000000e-01 7 | -------------------------------------------------------------------------------- /results/eGRF_TPL_2D/para0001/para.txt: -------------------------------------------------------------------------------- 1 | # storage, trans_gmean, var, len_scale, hurst 2 | 1.000000000000000048e-04 3 | 1.000000000000000048e-04 4 | 1.000000000000000000e+00 5 | 1.000000000000000000e+01 6 | 9.000000000000000222e-01 7 | -------------------------------------------------------------------------------- /results/eGRF_TPL_2D/para0002/para.txt: -------------------------------------------------------------------------------- 1 | # storage, trans_gmean, var, len_scale, hurst 2 | 1.000000000000000048e-04 3 | 1.000000000000000048e-04 4 | 1.000000000000000000e+00 5 | 2.000000000000000000e+01 6 | 5.000000000000000000e-01 7 | -------------------------------------------------------------------------------- /results/eGRF_TPL_2D/para0003/para.txt: -------------------------------------------------------------------------------- 1 | # storage, trans_gmean, var, len_scale, hurst 2 | 1.000000000000000048e-04 3 | 1.000000000000000048e-04 4 | 1.000000000000000000e+00 5 | 2.000000000000000000e+01 6 | 9.000000000000000222e-01 7 | -------------------------------------------------------------------------------- /results/eGRF_TPL_2D/para0004/para.txt: -------------------------------------------------------------------------------- 1 | # storage, trans_gmean, var, len_scale, hurst 2 | 1.000000000000000048e-04 3 | 1.000000000000000048e-04 4 | 2.250000000000000000e+00 5 | 1.000000000000000000e+01 6 | 5.000000000000000000e-01 7 | -------------------------------------------------------------------------------- /results/eGRF_TPL_2D/para0005/para.txt: -------------------------------------------------------------------------------- 1 | # storage, trans_gmean, var, len_scale, hurst 2 | 1.000000000000000048e-04 3 | 1.000000000000000048e-04 4 | 2.250000000000000000e+00 5 | 1.000000000000000000e+01 6 | 9.000000000000000222e-01 7 | -------------------------------------------------------------------------------- /results/eGRF_TPL_2D/para0006/para.txt: -------------------------------------------------------------------------------- 1 | # storage, trans_gmean, var, len_scale, hurst 2 | 1.000000000000000048e-04 3 | 1.000000000000000048e-04 4 | 2.250000000000000000e+00 5 | 2.000000000000000000e+01 6 | 5.000000000000000000e-01 7 | -------------------------------------------------------------------------------- /results/eGRF_TPL_2D/para0007/para.txt: -------------------------------------------------------------------------------- 1 | # storage, trans_gmean, var, len_scale, hurst 2 | 1.000000000000000048e-04 3 | 1.000000000000000048e-04 4 | 2.250000000000000000e+00 5 | 2.000000000000000000e+01 6 | 9.000000000000000222e-01 7 | -------------------------------------------------------------------------------- /.zenodo.json: -------------------------------------------------------------------------------- 1 | { 2 | "license": "MIT", 3 | "language": "eng", 4 | "keywords": [ 5 | "Groundwater flow equation", 6 | "Groundwater", 7 | "Pumping test", 8 | "Pump test", 9 | "Aquifer analysis", 10 | "extended generalized radial flow model", 11 | "transient drawdown", 12 | "Python", 13 | "GeoStat-Framework" 14 | ], 15 | "creators": [ 16 | { 17 | "orcid": "0000-0001-9060-4008", 18 | "affiliation": "Helmholtz Centre for Environmental Research - UFZ", 19 | "name": "Sebastian M\u00fcller" 20 | }, 21 | { 22 | "orcid": "0000-0002-8783-6198", 23 | "affiliation": "Hydrogeology Group, Department of Earth Science, Utrecht University, Netherlands", 24 | "name": "Alraune Zech" 25 | } 26 | ] 27 | } 28 | -------------------------------------------------------------------------------- /results/eGRF_TPL_2D/time.txt: -------------------------------------------------------------------------------- 1 | 0.000000000000000000e+00 2 | 2.416837299855660870e-01 3 | 1.933469839884528696e+00 4 | 6.525460709610285903e+00 5 | 1.546775871907622957e+01 6 | 3.021046624819575754e+01 7 | 5.220368567688228723e+01 8 | 8.289751938504917916e+01 9 | 1.237420697526098365e+02 10 | 1.761874391594776625e+02 11 | 2.416837299855660603e+02 12 | 3.216810446107884331e+02 13 | 4.176294854150582978e+02 14 | 5.309791547782888301e+02 15 | 6.631801550803934333e+02 16 | 8.156825887012855674e+02 17 | 9.899365580208786923e+02 18 | 1.187392165419086268e+03 19 | 1.409499513275821300e+03 20 | 1.657708703970997703e+03 21 | 1.933469839884528483e+03 22 | 2.238233023396327098e+03 23 | 2.573448356886307465e+03 24 | 2.940565942734382133e+03 25 | 3.341035883320466382e+03 26 | 3.776308281024470944e+03 27 | 4.247833238226310641e+03 28 | 4.757060857305896207e+03 29 | 5.305441240643147466e+03 30 | 5.894424490617970150e+03 31 | 6.525460709610284539e+03 32 | 7.199999999999997272e+03 33 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2021 GeoStat-Examples 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /src/01_convergence.py: -------------------------------------------------------------------------------- 1 | import os 2 | import numpy as np 3 | import matplotlib as mpl 4 | from matplotlib import pyplot as plt 5 | from anaflow import ext_theis_tpl, ext_thiem_tpl 6 | 7 | plt.style.use('default') 8 | mpl.rc("text", usetex=True) 9 | mpl.rc('lines', linewidth=3.5) 10 | plt.close("all") 11 | fig = plt.figure(figsize=[5, 3]) 12 | ax = fig.add_subplot(1, 1, 1) 13 | 14 | time = 1e4 # time point for steady state 15 | len_scale = 3.0 # correlation length of the log-transmissivity 16 | KG = 1e-4 # the geometric mean of the transmissivity 17 | hurst = 0.5 # hurst coefficient 18 | var = 0.5 # variance of the log-transmissivity 19 | rate = -1e-4 # pumping rate 20 | dim = 1.5 # using a fractional dimension 21 | r_ref = 3 * len_scale # reference radius 22 | rad = np.geomspace(0.1, r_ref) # radius from the pumping well in [0, 4] 23 | 24 | head1 = ext_thiem_tpl(rad, r_ref, KG, len_scale, hurst, var, dim=dim, rate=rate) 25 | head2 = ext_theis_tpl(time, rad, 1e-4, KG, len_scale, hurst, var, dim=dim, rate=rate, r_bound=r_ref) 26 | head3 = ext_theis_tpl(time, rad, 1e-4, KG, len_scale, hurst, var, dim=dim, rate=rate) 27 | head3 -= head3[-1] # quasi-steady 28 | 29 | ax.plot(rad, head1, label="Ext. Thiem TPL (steady state)") 30 | ax.plot(rad, head2, label="Ext. Theis TPL bounded (t={})".format(time), linestyle="--") 31 | ax.plot(rad, head3, label="Ext. Theis TPL quasi-steady (t={})".format(time), linestyle=":", color="k") 32 | ax.set_xticks([0, len_scale, 2 * len_scale, 3 * len_scale]) 33 | ax.set_xticklabels(["$0$", "$\ell$", "$2\ell$", "$3\ell$"]) 34 | ax.set_ylim([-1.7, 0.2]) 35 | ax.set_xlim([-0.06 * len_scale, 3.06 * len_scale]) 36 | ax.set_yticks([-1.5, -1, -0.5, 0]) 37 | ax.set_xlabel("$r$ in $[m]$") 38 | ax.set_ylabel("$h(r)$ in $[m]$") 39 | ax.grid(linestyle=':') 40 | ax.legend() 41 | fig.tight_layout() 42 | fig.savefig(os.path.join("..", "results", "01_ext_theis_tpl_conv.pdf"), dpi=300) 43 | fig.show() 44 | -------------------------------------------------------------------------------- /src/00_ext_theis_tpl.py: -------------------------------------------------------------------------------- 1 | import os 2 | import numpy as np 3 | import matplotlib as mpl 4 | from matplotlib import pyplot as plt 5 | from anaflow import theis, ext_theis_tpl 6 | 7 | plt.style.use('default') 8 | mpl.rc("text", usetex=True) 9 | mpl.rc('lines', linewidth=2.5) 10 | plt.close("all") 11 | fig = plt.figure(figsize=[5, 3]) 12 | ax = fig.add_subplot(1, 1, 1) 13 | 14 | time_ticks = [] 15 | time_labels = [r"$t=10$s", r"$t=10$min", r"$t=10$h"] 16 | time = [10, 600, 36000] # 10s, 10min, 10h 17 | rad = np.geomspace(0.05, 4.2) # radial distance from the pumping well in [0, 4] 18 | S = 1e-4 # storage 19 | KG = 1e-4 # the geometric mean of the conductivity 20 | len_scale = 20.0 # upper bound for the length scale 21 | hurst = 0.5 # hurst coefficient 22 | var = 0.5 # variance of the log-conductivity 23 | rate = -1e-4 # pumping rate 24 | KH = KG * np.exp(-var / 2) # the harmonic mean of the conductivity 25 | 26 | head_KG = theis(time, rad, S, KG, rate) 27 | head_KH = theis(time, rad, S, KH, rate) 28 | head_ef = ext_theis_tpl( 29 | time=time, 30 | rad=rad, 31 | storage=S, 32 | cond_gmean=KG, 33 | len_scale=len_scale, 34 | hurst=hurst, 35 | var=var, 36 | rate=rate, 37 | ) 38 | for i, step in enumerate(time): 39 | label_TG = "Theis($K_G$)" if i == 0 else None 40 | label_TH = "Theis($K_H$)" if i == 0 else None 41 | label_ef = "Ext. Theis TPL" if i == 0 else None 42 | color = "C0" # + str(i + 1) 43 | ax.plot(rad, head_KG[i], label=label_TG, color=color, linestyle="--", alpha=0.7) 44 | ax.plot(rad, head_KH[i], label=label_TH, color=color, linestyle=":", alpha=0.7) 45 | ax.plot(rad, head_ef[i], label=label_ef, color=color) 46 | text_v = head_ef[i][-1] 47 | ax.annotate( 48 | time_labels[i], 49 | xy=(rad[-1], text_v), 50 | xytext=(rad[-1] + 0.1, text_v), 51 | verticalalignment="center", 52 | ) 53 | ax.set_xlim([-0.2, 4.2]) 54 | ax.set_xticks([0, 1, 2, 3, 4]) 55 | ax.set_ylim([-1.7, 0.1]) 56 | ax.set_yticks([-1.5, -1, -0.5, 0]) 57 | ax.set_xlabel("$r$ in $[m]$") 58 | ax.set_ylabel("$h(r)$ in $[m]$") 59 | ax.grid(linestyle=':') 60 | ax.legend() 61 | ylim = ax.get_ylim() 62 | fig.tight_layout() 63 | fig.savefig(os.path.join("..", "results", "00_ext_theis_tpl_2D.pdf"), dpi=300) 64 | fig.show() 65 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | info/ 2 | 3 | # Byte-compiled / optimized / DLL files 4 | __pycache__/ 5 | *.py[cod] 6 | *$py.class 7 | 8 | # C extensions 9 | *.so 10 | 11 | # Distribution / packaging 12 | .Python 13 | build/ 14 | develop-eggs/ 15 | dist/ 16 | downloads/ 17 | eggs/ 18 | .eggs/ 19 | lib/ 20 | lib64/ 21 | parts/ 22 | sdist/ 23 | var/ 24 | wheels/ 25 | pip-wheel-metadata/ 26 | share/python-wheels/ 27 | *.egg-info/ 28 | .installed.cfg 29 | *.egg 30 | MANIFEST 31 | 32 | # PyInstaller 33 | # Usually these files are written by a python script from a template 34 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 35 | *.manifest 36 | *.spec 37 | 38 | # Installer logs 39 | pip-log.txt 40 | pip-delete-this-directory.txt 41 | 42 | # Unit test / coverage reports 43 | htmlcov/ 44 | .tox/ 45 | .nox/ 46 | .coverage 47 | .coverage.* 48 | .cache 49 | nosetests.xml 50 | coverage.xml 51 | *.cover 52 | *.py,cover 53 | .hypothesis/ 54 | .pytest_cache/ 55 | 56 | # Translations 57 | *.mo 58 | *.pot 59 | 60 | # Django stuff: 61 | *.log 62 | local_settings.py 63 | db.sqlite3 64 | db.sqlite3-journal 65 | 66 | # Flask stuff: 67 | instance/ 68 | .webassets-cache 69 | 70 | # Scrapy stuff: 71 | .scrapy 72 | 73 | # Sphinx documentation 74 | docs/_build/ 75 | 76 | # PyBuilder 77 | target/ 78 | 79 | # Jupyter Notebook 80 | .ipynb_checkpoints 81 | 82 | # IPython 83 | profile_default/ 84 | ipython_config.py 85 | 86 | # pyenv 87 | .python-version 88 | 89 | # pipenv 90 | # According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. 91 | # However, in case of collaboration, if having platform-specific dependencies or dependencies 92 | # having no cross-platform support, pipenv may install dependencies that don't work, or not 93 | # install all needed dependencies. 94 | #Pipfile.lock 95 | 96 | # PEP 582; used by e.g. github.com/David-OConnor/pyflow 97 | __pypackages__/ 98 | 99 | # Celery stuff 100 | celerybeat-schedule 101 | celerybeat.pid 102 | 103 | # SageMath parsed files 104 | *.sage.py 105 | 106 | # Environments 107 | .env 108 | .venv 109 | env/ 110 | venv/ 111 | ENV/ 112 | env.bak/ 113 | venv.bak/ 114 | 115 | # Spyder project settings 116 | .spyderproject 117 | .spyproject 118 | 119 | # Rope project settings 120 | .ropeproject 121 | 122 | # mkdocs documentation 123 | /site 124 | 125 | # mypy 126 | .mypy_cache/ 127 | .dmypy.json 128 | dmypy.json 129 | 130 | # Pyre type checker 131 | .pyre/ 132 | 133 | # simulation results 134 | results/**/seed* 135 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | [![GS-Frame](https://img.shields.io/badge/github-GeoStat_Framework-468a88?logo=github&style=flat)](https://github.com/GeoStat-Framework) 2 | [![Gitter](https://badges.gitter.im/GeoStat-Examples/community.svg)](https://gitter.im/GeoStat-Examples/community?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge) 3 | [![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.4246460.svg)](https://doi.org/10.5281/zenodo.4246460) 4 | 5 | # The eGRF model and its application to effective conductivity for TPL variograms 6 | 7 | 8 | ## Description 9 | 10 | The *extended* generalized radial flow (eGRF) model is an extension to the GRF model 11 | by allowing radial variable transmissivity and storativity values. 12 | The GRF model was derived by: 13 | 14 | > Barker, J.A., 1988. 15 | > A generalized radial flow model for hydraulic tests infractured rock. 16 | > Water Resources Research 24, 1796–1804. https://doi.org/10.1029/WR024i010p01796 17 | 18 | In this workflow, we demonstrate the abilities of the eGRF model and numerically 19 | prove, that the effective transmissivity for truncated power law (TPL) variograms 20 | reproduces the ensemble mean drawdown of pumping tests on synthetic aquifers. 21 | 22 | 23 | ## Structure 24 | 25 | The workflow is organized by the following structure: 26 | - `src/` - here you should place your python scripts 27 | - `00_ext_theis_tpl.py` - plotting the effective head for TPL variograms 28 | - `01_est_run.sh` - bash file running `02_para_estimation.py` in parallel 29 | - `01_convergence.py` - demonstating the convergence of the effective TPL solution 30 | - `02_step_function.py` - plot different step function approximations 31 | - `03_literature_transmissivities.py` - comparision of drawdowns for different 32 | transimissivites from literature 33 | - `04_trans_plot.py` - plot a realization of a TPL transmissivity field 34 | - `05_KTPL_plot.py` - plot K_TPL for different dimensions 35 | - `06_tplgaussian_vs_matern.py` - comparison of TPL-Gaussian and Matern models 36 | - `comparison/` - scripts for the comparison of ensemble mean to effective TPL heads 37 | - `00_run_sim_mpi.sh` - bash file running `01_run_sim.py` in parallel 38 | - `01_run_sim.py` - run all ensemble simulations for pumping tests on TPL aquifers 39 | - `02_compare_mean.py` - generate comparision plots for the ensemble means 40 | - `results/` - all produced results 41 | 42 | 43 | ## Python environment 44 | 45 | Main Python dependencies are stored in `requirements.txt`: 46 | 47 | ``` 48 | gstools==1.3.0 49 | anaflow==1.0.1 50 | ogs5py==1.1.1 51 | matplotlib 52 | ``` 53 | 54 | You can install them with `pip` (potentially in a virtual environment): 55 | 56 | ```bash 57 | pip install -r requirements.txt 58 | ``` 59 | 60 | 61 | ## Contact 62 | 63 | You can contact us via . 64 | 65 | 66 | ## License 67 | 68 | MIT © 2021 69 | -------------------------------------------------------------------------------- /results/eGRF_TPL_2D/rad.txt: -------------------------------------------------------------------------------- 1 | 0.000000000000000000e+00 2 | 1.030610152128364106e-03 3 | 8.244881217026912845e-03 4 | 2.782647410746583172e-02 5 | 6.595904973621530276e-02 6 | 1.288262690160455193e-01 7 | 2.226117928597266538e-01 8 | 3.534992821800288509e-01 9 | 5.276723978897224221e-01 10 | 7.513148009015774287e-01 11 | 1.030610152128364154e+00 12 | 1.371742112482852605e+00 13 | 1.780894342877813230e+00 14 | 2.264250504226015703e+00 15 | 2.827994257440230808e+00 16 | 3.478309263433228882e+00 17 | 4.221379183117779377e+00 18 | 5.063387677406653076e+00 19 | 6.010518407212619429e+00 20 | 7.068955033448449221e+00 21 | 8.244881217026913234e+00 22 | 9.544480618860783139e+00 23 | 1.097393689986282084e+01 24 | 1.253943372094580155e+01 25 | 1.424715474302250584e+01 26 | 1.610328362700569116e+01 27 | 1.811400403380812563e+01 28 | 2.028549962434258447e+01 29 | 2.262395405952184646e+01 30 | 2.513555100025867617e+01 31 | 2.782647410746583105e+01 32 | 3.070290704205608634e+01 33 | 3.377103346494223501e+01 34 | 3.703703703703702388e+01 35 | 4.050710141925322461e+01 36 | 4.418741027250359821e+01 37 | 4.808414725770095544e+01 38 | 5.220349603575803599e+01 39 | 5.655164026758759377e+01 40 | 6.113476361410241822e+01 41 | 6.595904973621530587e+01 42 | 7.103068229483899643e+01 43 | 7.635584495088626511e+01 44 | 8.194072136526982320e+01 45 | 8.779149519890256670e+01 46 | 9.391435011269719269e+01 47 | 1.003154697675664124e+02 48 | 1.070010378244231219e+02 49 | 1.139772379441800467e+02 50 | 1.212502537877499265e+02 51 | 1.288262690160455293e+02 52 | 1.367114672899795949e+02 53 | 1.449120322704650050e+02 54 | 1.534341476184144710e+02 55 | 1.622839969947406757e+02 56 | 1.714677640603565578e+02 57 | 1.809916324761747717e+02 58 | 1.908617859031081423e+02 59 | 2.010844080020694093e+02 60 | 2.116656824339712557e+02 61 | 2.226117928597266484e+02 62 | 2.339289229402482420e+02 63 | 2.456232563364486907e+02 64 | 2.577009767092410470e+02 65 | 2.701682677195378801e+02 66 | 2.830313130282519865e+02 67 | 2.962962962962961910e+02 68 | 3.099694011845831483e+02 69 | 3.240568113540257968e+02 70 | 3.385647104655367912e+02 71 | 3.534992821800287857e+02 72 | 3.688667101584148895e+02 73 | 3.846731780616076435e+02 74 | 4.009248695505198157e+02 75 | 4.176279682860642879e+02 76 | 4.347886579291535440e+02 77 | 4.524131221407007502e+02 78 | 4.705075445816185038e+02 79 | 4.890781089128193457e+02 80 | 5.081309987952164420e+02 81 | 5.276723978897224470e+02 82 | 5.477084898572497877e+02 83 | 5.682454583587119714e+02 84 | 5.892894870550209134e+02 85 | 6.108467596070901209e+02 86 | 6.329234596758316229e+02 87 | 6.555257709221585856e+02 88 | 6.786598770069842885e+02 89 | 7.023319615912205336e+02 90 | 7.265482083357804868e+02 91 | 7.513148009015775415e+02 92 | 7.766379229495233858e+02 93 | 8.025237581405312994e+02 94 | 8.289784901355145621e+02 95 | 8.560083025953849756e+02 96 | 8.836193791810563880e+02 97 | 9.118179035534403738e+02 98 | 9.406100593734502127e+02 99 | 9.700020303019994117e+02 100 | 9.999999999999994316e+02 101 | -------------------------------------------------------------------------------- /src/04_trans_plot.py: -------------------------------------------------------------------------------- 1 | """Generate a TPL field with GSTools.""" 2 | import os 3 | import numpy as np 4 | from ogs5py import MSH, specialrange 5 | import gstools as gs 6 | import matplotlib as mpl 7 | from matplotlib import pyplot as plt 8 | import matplotlib.tri as tri 9 | from mpl_toolkits.axes_grid1.inset_locator import zoomed_inset_axes 10 | from mpl_toolkits.axes_grid1.inset_locator import mark_inset 11 | 12 | plt.close("all") 13 | plt.style.use('default') 14 | mpl.rc("text", usetex=True) 15 | mpl.rc('lines', linewidth=3.5) 16 | fig = plt.figure(figsize=[5, 4]) 17 | ax = fig.add_subplot(1, 1, 1) 18 | 19 | # parameter lists to generate the para_set (single one) 20 | TG = 1e-4 # mu = log(TG) 21 | var = 1.0 ** 2 22 | len_scale = 10 23 | hurst = 0.5 24 | 25 | # radial discretization: 1000 m with 100 steps and increasing stepsize 26 | rad = specialrange(0, 1000, 100, typ="cub") 27 | # 64 angles for discretization 28 | angles = 64 29 | msh = MSH() 30 | msh.generate("radial", dim=2, angles=angles, rad=rad) 31 | 32 | seed = 1001 33 | # init cov model (truncated power law with gaussian modes) 34 | cov = gs.TPLGaussian(dim=2, var=var, len_scale=len_scale, hurst=hurst) 35 | # init spatial random field class 36 | srf = gs.SRF(cov, mean=np.log(TG), upscaling="coarse_graining") 37 | # generate new transmissivity field 38 | srf.mesh(msh, seed=seed, point_volumes=msh.volumes_flat) 39 | triang = tri.Triangulation(srf.pos[0], srf.pos[1]) 40 | field = srf.field.ravel() 41 | 42 | field[-56] = np.log(1e-2) + .1 # artificial value for colorbar fix (high-bound) 43 | field[-55] = np.log(1e-6) - .1 # artificial value for colorbar fix (low-bound) 44 | ticks = [np.log(10 ** i) for i in range(-6, 1)] # log-scale values 45 | labels = [r"$10^{" + str(i) + r"}$" for i in range(-6, 1)] 46 | levels=24 47 | 48 | ax.tricontour(triang, field, zorder=-10, levels=levels) # anti-alias 49 | cont1 = ax.tricontourf(triang, field, levels=levels) 50 | circle = plt.Circle((0, 0), 990, linewidth=1.5, color='k', fill=False) 51 | ax.add_artist(circle) 52 | cbar = fig.colorbar(cont1, ticks=ticks) 53 | cbar.ax.set_yticklabels(labels) 54 | cbar.ax.set_ylabel(r"transmissivity $T$ in $\left[\frac{m^2}{s}\right]$") 55 | ax.set_aspect("equal") 56 | ax.set_xticks([-1000, -500, 0, 500, 1000]) 57 | ax.set_yticks([-1000, -500, 0, 500, 1000]) 58 | ax.set_xlabel("$x$ in $[m]$") 59 | ax.set_ylabel("$y$ in $[m]$", labelpad=-10) 60 | 61 | axins = zoomed_inset_axes(ax, zoom=8.5, loc=1) 62 | axins.tricontour(triang, field, zorder=-10, levels=levels) # anti-alias 63 | cont2 = axins.tricontourf(triang, field, levels=levels) 64 | axins.scatter(0, 0, 5, color="k") 65 | axins.annotate(r"well", (5, -2)) 66 | axins.text( 67 | *(.98, .02, r"$100m\times 100m$"), 68 | fontsize=8, 69 | transform=axins.transAxes, 70 | horizontalalignment="right", 71 | ) 72 | axins.set_xlim(-50, 50) 73 | axins.set_ylim(-50, 50) 74 | axins.set_xticks([]) 75 | axins.set_yticks([]) 76 | 77 | mark_inset(ax, axins, loc1=2, loc2=4, fc="none", ec="k") 78 | 79 | # anti-alias 80 | for c in cont1.collections: 81 | c.set_edgecolor("face") 82 | for c in cont2.collections: 83 | c.set_edgecolor("face") 84 | 85 | fig.tight_layout() 86 | fig.savefig(os.path.join("..", "results", "04_trans_plot.pdf"), dpi=300) 87 | fig.show() 88 | -------------------------------------------------------------------------------- /src/02_step_function.py: -------------------------------------------------------------------------------- 1 | import os 2 | import numpy as np 3 | import matplotlib as mpl 4 | from matplotlib import pyplot as plt 5 | from anaflow.tools.coarse_graining import TPL_CG, TPL_CG_error, T_CG, T_CG_error 6 | from anaflow.tools.mean import annular_hmean 7 | from anaflow.tools.special import specialrange_cut, specialrange, step_f 8 | 9 | plt.style.use('default') 10 | mpl.rc("text", usetex=True) 11 | mpl.rc('lines', linewidth=3.5) 12 | plt.close("all") 13 | fig = plt.figure(figsize=[5, 3]) 14 | ax = fig.add_subplot(1, 1, 1) 15 | 16 | cond_gmean = 1e-4 # the geometric mean of the transmissivity 17 | len_scale = 5.0 # correlation length of the log-transmissivity 18 | hurst = 0.5 # hurst coefficient 19 | var = 1.0 # variance of the log-transmissivity 20 | rate = -1e-4 # pumping rate 21 | dim = 2.0 # using a fractional dimension 22 | 23 | far_err = 0.01 # absolute error for cut-off 24 | parts = 20 # number of partitions 25 | 26 | # genearte rlast from a given relativ-error to farfield-conductivity 27 | r_last_tpl = TPL_CG_error(far_err, cond_gmean, len_scale, hurst, var, dim=dim) 28 | # generate the partition points (with cut-off) 29 | R_part_tpl = specialrange_cut(0, np.inf, parts + 1, r_last_tpl) 30 | # calculate the harmonic mean conductivity values within each partition 31 | K_part_tpl = annular_hmean( 32 | TPL_CG, 33 | R_part_tpl, 34 | ann_dim=dim, 35 | cond_gmean=cond_gmean, 36 | len_scale=len_scale, 37 | hurst=hurst, 38 | var=var, 39 | dim=dim, 40 | ) 41 | 42 | # genearte rlast from a given relativ-error to farfield-conductivity 43 | r_last = T_CG_error(far_err, cond_gmean, var, len_scale) 44 | # generate the partition points 45 | R_part = specialrange_cut(0, np.inf, parts + 1, r_last) 46 | # calculate the harmonic mean conductivity values within each partition 47 | K_part = annular_hmean( 48 | T_CG, 49 | R_part, 50 | ann_dim=dim, 51 | trans_gmean=cond_gmean, 52 | var=var, 53 | len_scale=len_scale, 54 | ) 55 | 56 | rad = specialrange(0, 3 * len_scale, 1000) 57 | 58 | ax.plot( 59 | rad, 60 | step_f(rad, R_part_tpl, K_part_tpl), 61 | color="C0", 62 | linewidth=3.5, 63 | solid_joinstyle="miter", 64 | label="$T_{\mathrm{TPL}}$ - truncated power law", 65 | ) 66 | ax.plot( 67 | rad, 68 | TPL_CG(rad, cond_gmean, len_scale, hurst, var, dim=dim), 69 | color="k", 70 | linewidth=2, 71 | alpha=0.6, 72 | ) 73 | 74 | ax.plot( 75 | rad, 76 | step_f(rad, R_part, K_part), 77 | color="C1", 78 | linewidth=3.5, 79 | solid_joinstyle="miter", 80 | label="$T_{\mathrm{RCG}}$ - gaussian", 81 | ) 82 | ax.plot( 83 | rad, 84 | T_CG(rad, cond_gmean, var, len_scale), 85 | color="k", 86 | linewidth=2, 87 | alpha=0.6, 88 | ) 89 | 90 | ax.ticklabel_format(axis='y', style='scientific', scilimits=(-4, -4)) 91 | ax.set_xlim([-0.06 * len_scale, 3.06 * len_scale]) 92 | ax.set_xticks([0, len_scale, 2 * len_scale, 3 * len_scale]) 93 | ax.set_xticklabels(["$0$", "$\ell$", "$2\ell$", "$3\ell$"]) 94 | 95 | ax.set_xlabel("$r$ in $[m]$") 96 | ax.set_ylabel("$T(r)$ in $[m^2 / s]$") 97 | ax.grid(linestyle=':') 98 | ax.legend() 99 | 100 | fig.tight_layout() 101 | fig.savefig( 102 | os.path.join("..", "results", "02_step_functions.pdf"), dpi=300 103 | ) 104 | fig.show() 105 | -------------------------------------------------------------------------------- /src/05_KTPL_plot.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """ 3 | Plot showing the effective well flow conductivity K_TPL(r) with 4 | truncated power law (TPL) variogram in a fractal dimension (d=2.5). 5 | 6 | It is compared to its approximation as step function, which serves the 7 | numerical solution of the groundwater flow equation 8 | under radial flow conditions according to the extended Theis TPL method. 9 | 10 | K_TPL(r) was derived making use of the upscaling Method Coarse Graining as 11 | extension of the effective well flow conductivity T_CG(r) a with 12 | Gaussian variogram. 13 | It interpolates between the representative conductivity values for pumping 14 | tests flow setting: 15 | - K_H as near well average representative (considering constant head BC) 16 | - K_efu (of uniform flow) as far field average representative, which is 17 | depending on the considered dimension: 18 | K_efu (2D) = K_G (geometric mean) 19 | K_efu (3D) = K_G exp(1/6 sigma^2) [for isotropic media] 20 | K_efu (d) = K_G exp((1/2 - 1/d) sigma^2) [for isotropic media], 21 | representing also fractional dimension such as d = 2.5 chosen here 22 | The transition is a function of radial distance to the well r and is controlled 23 | by the stastisitical parameters of the underlying log-normal conducitivity and 24 | its variogram properties: variance $\sigma^2$, correlation length $\all$ and 25 | Hurst coefficient $H$. 26 | """ 27 | 28 | import os 29 | import numpy as np 30 | from matplotlib import pyplot as plt 31 | import matplotlib as mpl 32 | from anaflow.tools.coarse_graining import TPL_CG 33 | 34 | ############################################################################### 35 | ### Plot Settings 36 | plt.style.use("default") 37 | mpl.rc("text", usetex=True) 38 | mpl.rc("lines", linewidth=2.5) 39 | plt.close("all") 40 | fig = plt.figure(figsize=[5, 3]) 41 | ax = fig.add_subplot(1, 1, 1) 42 | 43 | ############################################################################### 44 | ### Parameter Settings 45 | cond_gmean = 1e-4 # the geometric mean of the transmissivity 46 | len_scale = 5.0 # correlation length of the log-transmissivity 47 | hurst = 0.5 # hurst coefficient 48 | var = 1.0 # variance of the log-transmissivity 49 | 50 | rad = np.linspace(0, 3 * len_scale, 1000) 51 | K_H = np.exp(-var / 2) 52 | 53 | ############################################################################### 54 | ### Plotting 55 | for dim in [3, 2.5, 2]: 56 | ax.plot( 57 | rad, 58 | TPL_CG(rad, cond_gmean, len_scale, hurst, var, dim=dim) / cond_gmean, 59 | label="$K_{{TPL}}(r)$ (d = {})".format(dim), 60 | ) 61 | K_efu = np.exp(var * (0.5 - 1 / dim)) 62 | 63 | ax.plot(rad, K_efu * np.ones_like(rad), "k--", lw=1) 64 | ax.text( 65 | rad[-1], 66 | 1.01 * K_efu, 67 | "$K_{{\mathrm{{efu}}}}/K_G$ ({}D)".format(dim), 68 | horizontalalignment="right", 69 | ) 70 | 71 | ax.plot(rad, K_H * np.ones_like(rad), "k--", lw=1) 72 | ax.text( 73 | rad[-1], 74 | 1.01 * K_H, 75 | "$K_{\mathrm{well}}/K_G$", 76 | horizontalalignment="right", 77 | ) 78 | 79 | ax.set_ylim(0.58, 1.25) 80 | ax.set_ylabel("$K(r)/K_G$") 81 | ax.set_xlim([-0.06 * len_scale, 3.06 * len_scale]) 82 | ax.set_xticks([0, len_scale, 2 * len_scale, 3 * len_scale]) 83 | ax.set_xticklabels(["$0$", "$\ell$", "$2\ell$", "$3\ell$"]) 84 | ax.set_xlabel("$r$ in $[m]$") 85 | 86 | ax.grid(linestyle=":") 87 | # ax.legend(loc=(0.59, 0.21)) 88 | 89 | fig.tight_layout() 90 | fig.savefig(os.path.join("..", "results", "05_KTPL.pdf"), dpi=300) 91 | fig.show() 92 | -------------------------------------------------------------------------------- /src/06_tplgaussian_vs_matern.py: -------------------------------------------------------------------------------- 1 | """TPL-Gaussian model vs. Matern model family.""" 2 | import os 3 | import numpy as np 4 | import matplotlib as mpl 5 | from matplotlib import pyplot as plt 6 | import gstools as gs 7 | 8 | plt.style.use("default") 9 | mpl.rc("text", usetex=True) 10 | mpl.rc("lines", linewidth=3.5) 11 | plt.close("all") 12 | 13 | 14 | def dashes(i=1, max_d=12, space=1): 15 | """Dashes for matplotlib.""" 16 | return i * [space, space] + [max_d - 2 * i * space, space] 17 | 18 | 19 | def format_ax(axis): 20 | """Format axis.""" 21 | axis.set_xlim([-0.06, 3.06]) 22 | axis.set_xticks(range(4)) 23 | axis.set_xticklabels(["$0$", r"$\ell$", r"$2\ell$", r"$3\ell$"]) 24 | axis.set_xlabel("distance") 25 | axis.set_ylabel("semivariance") 26 | axis.set_ylim([0, 1]) 27 | axis.grid(linestyle=":") 28 | axis.legend() 29 | 30 | 31 | save = True 32 | x = np.geomspace(0.01, 3, 10) 33 | grid = np.linspace(0, 10, 100) 34 | 35 | # Matern(nu=1.5) vs TPL-Gaussian 36 | 37 | fig, ax = plt.subplots(figsize=[5, 3]) 38 | 39 | m1 = gs.Matern(dim=2, integral_scale=1, nu=1.5) 40 | fit_m1 = gs.TPLGaussian(dim=2) 41 | fit_m1.fit_variogram(x, m1.variogram(x), len_low=0, nugget=0) 42 | m1.plot(ax=ax, x_max=3, label="Matern(nu=1.5)", color="k", linewidth=2) 43 | fit_m1.plot( 44 | ax=ax, x_max=3, label="TPL-Gaussian(hurst=1.0)", linestyle=":", color="C0" 45 | ) 46 | 47 | print(m1) 48 | print(fit_m1) 49 | 50 | format_ax(ax) 51 | fig.tight_layout() 52 | if save: 53 | fig.savefig( 54 | os.path.join("..", "results", "06_matern_tpl_1-5.pdf"), dpi=300 55 | ) 56 | fig.show() 57 | 58 | # Matern(nu=0.5) vs TPL-Gaussian 59 | 60 | fig, ax = plt.subplots(figsize=[5, 3]) 61 | 62 | m2 = gs.Matern(dim=2, integral_scale=1, nu=0.5) 63 | fit_m2 = gs.TPLGaussian(dim=2) 64 | fit_m2.fit_variogram(x, m2.variogram(x), len_low=0, nugget=0) 65 | m2.plot(ax=ax, x_max=3, label="Matern(nu=0.5)", color="k", linewidth=2) 66 | fit_m2.plot( 67 | ax=ax, x_max=3, label="TPL-Gaussian(hurst=0.45)", linestyle=":", color="C0" 68 | ) 69 | 70 | print(m2) 71 | print(fit_m2) 72 | 73 | format_ax(ax) 74 | fig.tight_layout() 75 | if save: 76 | fig.savefig( 77 | os.path.join("..", "results", "07_matern_tpl_0-5.pdf"), dpi=300 78 | ) 79 | fig.show() 80 | 81 | # model families 82 | 83 | fig, ax = plt.subplots(figsize=[5, 3]) 84 | 85 | gau = gs.Gaussian(integral_scale=1) 86 | exp = gs.Exponential(integral_scale=1) 87 | nus = [0.5, 0.75, 1.0, 1.5, 2.0] 88 | # ax = exp.plot(ax=ax, x_max=3, linestyle="-.", color="k") 89 | ax = gau.plot(ax=ax, x_max=3, linestyle="-", color="k") 90 | for i, nu in enumerate(nus): 91 | m = gs.Matern(integral_scale=1, nu=nu) 92 | ax = m.plot( 93 | ax=ax, 94 | x_max=3, 95 | label=f"Matern(nu={nu:.2})", 96 | linewidth=2, 97 | dashes=dashes(i), 98 | color="C0", 99 | ) 100 | format_ax(ax) 101 | fig.tight_layout() 102 | if save: 103 | fig.savefig(os.path.join("..", "results", "08_matern_family.pdf"), dpi=300) 104 | fig.show() 105 | 106 | fig, ax = plt.subplots(figsize=[5, 3]) 107 | 108 | hursts = [0.45, 0.5, 0.6, 0.8, 0.999] 109 | # ax = exp.plot(ax=ax, x_max=3, linestyle="-.", color="k") 110 | ax = gau.plot(ax=ax, x_max=3, linestyle="-", color="k") 111 | for i, hurst in enumerate(hursts): 112 | m = gs.TPLGaussian(integral_scale=1, hurst=hurst) 113 | ax = m.plot( 114 | ax=ax, 115 | x_max=3, 116 | label=f"TPL-Gaussian(hurst={hurst:.2})", 117 | linewidth=2, 118 | dashes=dashes(i), 119 | color="C0", 120 | ) 121 | format_ax(ax) 122 | fig.tight_layout() 123 | if save: 124 | fig.savefig(os.path.join("..", "results", "09_tpl_family.pdf"), dpi=300) 125 | fig.show() 126 | 127 | # Fields 128 | 129 | fig, ax = plt.subplots(figsize=[5, 4]) 130 | srf = gs.SRF(m1, seed=1234) 131 | field1a = srf.structured((grid, grid)) 132 | srf.plot(ax=ax, contour_plot=False) 133 | ax.set_title("Matern(nu=1.5)") 134 | fig.tight_layout() 135 | if save: 136 | fig.savefig( 137 | os.path.join("..", "results", "10_field_matern_1-5.pdf"), dpi=300 138 | ) 139 | fig.show() 140 | 141 | fig, ax = plt.subplots(figsize=[5, 4]) 142 | srf = gs.SRF(m2, seed=1234) 143 | srf.structured((grid, grid)) 144 | srf.plot(ax=ax, contour_plot=False) 145 | ax.set_title("Matern(nu=0.5)") 146 | fig.tight_layout() 147 | if save: 148 | fig.savefig( 149 | os.path.join("..", "results", "11_field_matern_0-5.pdf"), dpi=300 150 | ) 151 | fig.show() 152 | -------------------------------------------------------------------------------- /src/comparison/02_compare_mean.py: -------------------------------------------------------------------------------- 1 | """Post processing the TPL ensembles.""" 2 | import os 3 | import glob 4 | import numpy as np 5 | from mpl_toolkits.mplot3d import Axes3D 6 | import matplotlib.pyplot as plt 7 | from matplotlib import cm, rc 8 | import anaflow as ana 9 | from PyPDF2 import PdfFileMerger 10 | 11 | 12 | rc("text", usetex=True) 13 | CWD = os.path.abspath(os.path.join("..", "..", "results")) 14 | 15 | 16 | def calc_ensemble_mean(base="eGRF_TPL_2D", p_min=0, p_max=np.inf): 17 | """Generate mean for all simulations in ensemble from single means.""" 18 | para_sets = sorted(glob.glob(os.path.join(CWD, base, "para*"))) 19 | time = np.loadtxt(os.path.join(CWD, base, "time.txt")) 20 | rad = np.loadtxt(os.path.join(CWD, base, "rad.txt")) 21 | # iterate over all parameter sets 22 | for para_no, para_set in enumerate(para_sets): 23 | if para_no < p_min or para_no > p_max: 24 | continue 25 | print(para_no, "PARA_SET: ensemble mean calculation") 26 | ensemble = sorted(glob.glob(os.path.join(para_set, "seed*"))) 27 | rt_head = np.zeros(time.shape + rad.shape, dtype=float) 28 | # collect all ensemble members 29 | for cnt, single in enumerate(ensemble, start=1): 30 | sgl_head = np.loadtxt(os.path.join(single, "rad_mean_head.txt")) 31 | if cnt % 50 == 0: 32 | print(" para-Set", para_no, ": member", cnt) 33 | rt_head += sgl_head 34 | # ensemble mean 35 | if ensemble: # skip if ensemble is empty 36 | print(" --> write file 'rad_mean_head.txt'") 37 | rt_head /= len(ensemble) 38 | np.savetxt(os.path.join(para_set, "rad_mean_head.txt"), rt_head) 39 | 40 | 41 | def compare(base="eGRF_TPL_2D", p_min=0, p_max=np.inf): 42 | """Compare ensemble mean to effective drawdown solution.""" 43 | path = os.path.join(CWD, base) 44 | para_sets = sorted(glob.glob(os.path.join(path, "para*"))) 45 | time = np.loadtxt(os.path.join(path, "time.txt")) 46 | rad = np.loadtxt(os.path.join(path, "rad.txt")) 47 | time_range = time > 60 48 | rad_range = np.logical_and(rad > 0.2, rad < 40) 49 | time_select = time[time_range] 50 | rad_select = rad[rad_range] 51 | # iterate over all parameter sets 52 | for para_no, para_set in enumerate(para_sets): 53 | if para_no < p_min or para_no > p_max: 54 | continue 55 | para = np.loadtxt(os.path.join(para_set, "para.txt")) 56 | rt_head = np.loadtxt(os.path.join(para_set, "rad_mean_head.txt")) 57 | print(para_no, "PARA_SET") 58 | rt_head = rt_head[time_range] 59 | rt_head = rt_head[:, rad_range] 60 | et_head = ana.ext_theis_tpl( # effective transmissivity 61 | time=time_select, 62 | rad=rad_select, 63 | storage=para[0], 64 | cond_gmean=para[1], 65 | var=para[2], 66 | len_scale=para[3], 67 | hurst=para[4], 68 | rate=-1e-4, 69 | parts=30, 70 | # gaussian covmodel in GSTools normalized to integral scale 71 | prop=np.sqrt(np.pi * 2), 72 | ) 73 | # print relative errors 74 | abs_diff = np.abs(rt_head - et_head) 75 | abs_mean = 0.5 * (np.abs(rt_head) + np.abs(et_head)) 76 | rel_diff = abs_diff / np.max(abs_mean) 77 | print(" max rel. diff:", np.max(rel_diff)) 78 | # creat plots 79 | plot_diff( 80 | time_select, rad_select, rt_head, et_head, para_no, path, para 81 | ) 82 | # merge pdfs 83 | pdfs = sorted(glob.glob(os.path.join(path, "*_diff.pdf"))) 84 | merger = PdfFileMerger() 85 | for pdf in pdfs: 86 | merger.append(pdf) 87 | merger.write(os.path.join(path, "diff.pdf")) 88 | # for pdf in pdfs: 89 | # os.remove(pdf) 90 | 91 | 92 | def plot_diff(time, rad, rt_head, et_head, para_no, path, para): 93 | """Plot the comparisson between effective head and ensemble mean.""" 94 | plt.close("all") 95 | fig = plt.figure(figsize=[10, 3.4]) 96 | ax0 = plt.subplot2grid((1, 3), (0, 0), fig=fig, projection=Axes3D.name) 97 | ax1 = plt.subplot2grid((1, 3), (0, 2), fig=fig, projection=Axes3D.name) 98 | ax2 = plt.subplot2grid((1, 3), (0, 1), fig=fig, projection=Axes3D.name) 99 | 100 | time_m, rad_m = np.meshgrid(time, rad, indexing="ij") 101 | diff = np.abs(rt_head - et_head) 102 | z_max = 0.1 103 | z_min = -2.1 104 | 105 | ax0.plot_surface( 106 | rad_m, 107 | time_m, 108 | rt_head, 109 | rstride=1, 110 | cstride=1, 111 | cmap=cm.RdBu, 112 | linewidth=0.3, 113 | antialiased=True, 114 | edgecolors="k", 115 | ) 116 | ax1.plot_surface( 117 | rad_m, 118 | time_m, 119 | et_head, 120 | rstride=1, 121 | cstride=1, 122 | cmap=cm.RdBu, 123 | linewidth=0.3, 124 | antialiased=True, 125 | edgecolors="k", 126 | ) 127 | ax2.plot_surface( 128 | rad_m, 129 | time_m, 130 | diff, 131 | rstride=1, 132 | cstride=1, 133 | cmap=cm.RdBu_r, 134 | linewidth=0.3, 135 | antialiased=True, 136 | edgecolors="k", 137 | vmin=0, vmax=1, 138 | ) 139 | ax2.plot_surface( 140 | rad_m, 141 | time_m, 142 | np.zeros_like(diff), 143 | rstride=1, 144 | cstride=1, 145 | color="k", 146 | alpha=0.4, 147 | antialiased=True, 148 | ) 149 | ax0.view_init(elev=15, azim=-150) 150 | ax1.view_init(elev=15, azim=-150) 151 | ax2.view_init(elev=15, azim=-150) 152 | fig.suptitle( 153 | r"Parameter set P{}: ".format(para_no) 154 | + r"$S={:.1e}".format(para[0]) 155 | + r"$, $T_G={:.1e}".format(para[1]) 156 | + r"$, $\sigma^2={}".format(para[2]) 157 | + r"$, $\ell={}".format(para[3]) 158 | + r"$, $H={}".format(para[4]) 159 | + r"$" 160 | ) 161 | xlab = r"$r$ in $\mathrm{[m]}$" 162 | ylab = r"$t$ in $\mathrm{[s]}$" 163 | ax0.set_title("Ensemble mean drawdown in $\mathrm{[m]}$", pad=-5) 164 | ax1.set_title("Effective drawdown in $\mathrm{[m]}$", pad=-5) 165 | ax2.set_title("Absolute difference in $\mathrm{[m]}$", pad=-5) 166 | # change axes labels 167 | ax0.set_xlabel(xlab) 168 | ax0.set_ylabel(ylab) 169 | ax1.set_xlabel(xlab) 170 | ax1.set_ylabel(ylab) 171 | ax2.set_xlabel(xlab) 172 | ax2.set_ylabel(ylab) 173 | ax0.set_zlim((z_min, z_max)) 174 | ax1.set_zlim((z_min, z_max)) 175 | ax2.set_zlim((-1, 1)) 176 | fig.tight_layout() 177 | plt.savefig(os.path.join(path, "{:04}_diff.pdf".format(para_no)), dpi=300) 178 | plt.close("all") 179 | 180 | 181 | calc_ensemble_mean() 182 | compare() 183 | -------------------------------------------------------------------------------- /src/03_literature_transmissivities.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | import os 3 | import numpy as np 4 | from scipy import stats 5 | from matplotlib import pyplot as plt 6 | from matplotlib import rc 7 | from matplotlib.offsetbox import AnchoredText 8 | from anaflow import ext_grf, ext_grf_steady 9 | from anaflow.tools import neuman2004_trans, K_CG, T_CG 10 | from anaflow.tools import specialrange_cut, annular_hmean, step_f 11 | 12 | 13 | plt.style.use('default') 14 | rc("text", usetex=True) 15 | 16 | 17 | def dashes(i=1, max_n=12, width=1): 18 | """Dashes for matplotlib""" 19 | return i * [width, width] + [max_n * 2 * width - 2 * i * width, width] 20 | 21 | class sol_container: 22 | """Container to store all information about an eGRF solution.""" 23 | def __init__(self, r_part, t_part, storage, label, title, t_w=None, trans=None): 24 | self.step_trans = lambda r: step_f(r, r_part, t_part) 25 | self.step = trans is None 26 | if self.step: 27 | self.trans = self.step_trans 28 | else: 29 | self.trans = trans 30 | self.t_w = self.trans(0) if t_w is None else t_w 31 | self.r_part = r_part 32 | self.t_part = t_part 33 | self.s_part = np.full_like(t_part, storage) 34 | self.label = label 35 | self.title = title 36 | 37 | 38 | time_labels = [r"$t=10$s", r"$t=10$min", r"$t=10$h"] 39 | time = [10, 600, 36000] # 10s, 10min, 10h 40 | rad = np.geomspace(0.1, 9) 41 | rad_lin = np.linspace(0, rad[-1], 1000) 42 | S = 1e-3 43 | K_well = 2e-5 44 | K_far = 1e-4 45 | K_diff = K_far - K_well 46 | K_mean = stats.hmean((K_well, K_far)) # harmonic mean 47 | # variance to result in K_well in 2D 48 | var = -2 * np.log(K_well / K_far) 49 | # K_gmean to result in K_far in 3D with var=1 and anis=1 50 | K_g3d = K_far * np.exp(- 1. / 6.) 51 | len_scale = 3.0 52 | rate = -1e-4 53 | dim = 2 54 | 55 | cut_off = 2 * len_scale 56 | parts = 20 57 | r_well = 0.0 58 | r_bound = 50.0 59 | R_part = specialrange_cut(r_well, r_bound, parts, rad[-1]) 60 | solutions = [] 61 | # SOL 1: GRF with constant conductivity and differing well conductivity 62 | sol = sol_container( 63 | r_part=[r_well, r_bound], 64 | t_part=[K_far], 65 | t_w=K_far, 66 | storage=S, 67 | label=r"\textit{Barker (1988)}", 68 | title="A", 69 | ) 70 | solutions.append(sol) 71 | # SOL 2: Butler 1988: two zone aquifer 72 | sol = sol_container( 73 | r_part=[r_well, len_scale, r_bound], 74 | t_part=[K_well, K_far], 75 | t_w=K_well, 76 | storage=S, 77 | label=r"\textit{Butler (1988)}", 78 | title="B", 79 | ) 80 | solutions.append(sol) 81 | # SOL 3: Avci 2014: three (multi) zone aquifer 82 | sol = sol_container( 83 | r_part=[r_well, len_scale, cut_off, r_bound], 84 | t_part=[K_well, K_mean, K_far], 85 | t_w=K_well, 86 | storage=S, 87 | label=r"\textit{Avci \& Sahin (2014)}", 88 | title="C", 89 | ) 90 | solutions.append(sol) 91 | # SOL 4: Neuman 2004: apparent transmissivity 92 | sol = sol_container( 93 | trans=lambda r: neuman2004_trans(r, trans_gmean=K_far, var=var, len_scale=len_scale), 94 | r_part=R_part, 95 | t_part=annular_hmean(neuman2004_trans, R_part, ann_dim=2, trans_gmean=K_far, var=var, len_scale=len_scale), 96 | storage=S, 97 | label=r"\textit{Neuman et al. (2004)}", 98 | title="D", 99 | ) 100 | solutions.append(sol) 101 | # SOL 5: Schneider 2008: extended theis 2D 102 | sol = sol_container( 103 | trans=lambda r: T_CG(r, trans_gmean=K_far, var=var, T_well=K_well, len_scale=len_scale), 104 | r_part=R_part, 105 | t_part=annular_hmean(T_CG, R_part, ann_dim=2, trans_gmean=K_far, var=var, T_well=K_well, len_scale=len_scale), 106 | storage=S, 107 | label=r"\textit{Schneider \& Attinger (2008)}", 108 | title="E", 109 | ) 110 | solutions.append(sol) 111 | # SOL 6: Zech 2012: extended theis 3D 112 | sol = sol_container( 113 | trans=lambda r: K_CG(r, cond_gmean=K_g3d, var=1, anis=1, K_well=K_well, len_scale=len_scale), 114 | r_part=R_part, 115 | t_part=annular_hmean(K_CG, R_part, ann_dim=2, cond_gmean=K_g3d, var=1, anis=1, K_well=K_well, len_scale=len_scale), 116 | storage=S, 117 | label=r"\textit{Zech et al. (2012)}", 118 | title="F", 119 | ) 120 | solutions.append(sol) 121 | 122 | # PLOTTING 123 | plt.close("all") 124 | fig = plt.figure(figsize=[10, 5], constrained_layout=False) 125 | gs = fig.add_gridspec(2, 1) # two rows 126 | rows = [] 127 | rows.append(gs[0].subgridspec(2, 3, height_ratios=[1, 3], hspace=0, wspace=0.1)) 128 | rows.append(gs[1].subgridspec(2, 3, height_ratios=[1, 3], hspace=0, wspace=0.1)) 129 | # resulting axis pairs as flat list 130 | axis = [] 131 | # generate 6 axis with two rows 132 | for j in range(2): 133 | for i in range(3): 134 | ax = [] 135 | ax.append(fig.add_subplot(rows[j][0, i])) 136 | ax.append(fig.add_subplot(rows[j][1, i], sharex=ax[0])) 137 | plt.setp(ax[0].get_xticklabels(), visible=False) 138 | ax[0].set_yticks([K_well, K_far]) 139 | if i > 0: # only show y axis tick-labels for left axis 140 | plt.setp(ax[0].get_yticklabels(), visible=False) 141 | plt.setp(ax[1].get_yticklabels(), visible=False) 142 | else: 143 | ax[0].set_yticklabels(["$T_{\mathrm{well}}$", "$T_{\mathrm{far}}$"]) 144 | ax[1].set_ylabel(r"$h(r,t)$ in $[m]$") 145 | # if j == 1: 146 | # ax[1].set_xlabel(r"$r$ in $[m]$") 147 | if j == 0: # hide x axis tick-labels for the top row 148 | plt.setp(ax[1].get_xticklabels(), visible=False) 149 | ax[1].set_xticks([0, len_scale, cut_off, rad[-1]]) 150 | ax[1].set_xticklabels(["$0$", "$\ell$", "$2\ell$", "$3\ell$"]) 151 | axis.append(ax) 152 | # plot given solutions 153 | for i, sol in enumerate(solutions): 154 | axis[i][0].plot(rad_lin, sol.step_trans(rad_lin), label="transmissivity $T(r)$", linewidth=3.5, solid_joinstyle="miter") 155 | if not sol.step: 156 | axis[i][0].plot(rad_lin, sol.trans(rad_lin), linewidth=1, color="w", alpha=0.6) 157 | axis[i][0].set_ylim([K_well - 0.15 * K_diff, K_far + 0.15 * K_diff]) 158 | axis[i][0].set_title(sol.label) 159 | # timesteps 160 | head1 = ext_grf(time, rad, sol.s_part, sol.t_part, sol.r_part, K_well=sol.t_w, dim=dim, rate=rate) 161 | head2 = ext_grf_steady(rad, r_bound, sol.trans, dim=dim, rate=rate) 162 | for k, step in enumerate(time): 163 | axis[i][1].plot(rad, head1[k], dashes=dashes(i=k+1, max_n=9), alpha=1., label=time_labels[k], linewidth=3, color="k") 164 | axis[i][1].plot(rad, head2, label="steady state", linewidth=2.5, color="C1", alpha=1, zorder=-10) 165 | axis[i][1].set_ylim([-2.2, 0.2]) 166 | text_box = AnchoredText(sol.title, frameon=True, loc=4, pad=0.5) 167 | plt.setp(text_box.patch, facecolor='white', alpha=0.5) 168 | axis[i][1].add_artist(text_box) 169 | # axis[i][0].grid(axis="x", linestyle=':') 170 | axis[i][1].grid(linestyle=':') 171 | 172 | # create legend 173 | if i == 0: 174 | handles1, labels1 = axis[i][0].get_legend_handles_labels() 175 | handles2, labels2 = axis[i][1].get_legend_handles_labels() 176 | # add legend 177 | handles = handles1 + handles2 178 | labels = labels1 + labels2 179 | fig.legend(handles, labels, loc='lower center', ncol=5, handlelength=4.0) 180 | # tighten layout 181 | plt.tight_layout() 182 | fig.subplots_adjust(bottom=0.13) 183 | fig.savefig( 184 | os.path.join("..", "results", "03_literature_comparison.pdf"), dpi=300 185 | ) 186 | plt.show() 187 | -------------------------------------------------------------------------------- /src/comparison/01_run_sim.py: -------------------------------------------------------------------------------- 1 | """Generate a TPL ensemble of drawdowns with ogs5py and GSTools.""" 2 | import os 3 | import shutil 4 | import numpy as np 5 | from ogs5py import OGS, specialrange, generate_time, by_id 6 | from ogs5py.reader import readpvd 7 | import gstools as gs 8 | from gstools import transform as tf 9 | from mpi4py import MPI 10 | 11 | 12 | def angles_mean(time, rad, angles, path): 13 | """Generate mean along angles for single simulation.""" 14 | # read output from ogs5py 15 | out = readpvd(task_root=path, task_id="model", pcs="GROUNDWATER_FLOW") 16 | rt_head = np.zeros(time.shape + rad.shape, dtype=float) 17 | # loop over time 18 | for select, step in enumerate(time): 19 | points = out["DATA"][select]["points"] 20 | radii = np.sqrt(points[:, 0] ** 2 + points[:, 1] ** 2) 21 | rad_ids = np.argmin(np.abs(np.subtract.outer(rad, radii)), axis=0) 22 | for i, head in enumerate(out["DATA"][select]["point_data"]["HEAD"]): 23 | rt_head[select, rad_ids[i]] += head 24 | # only one head value for rad=0 25 | rt_head[:, 1:] = rt_head[:, 1:] / angles 26 | np.savetxt(os.path.join(path, "rad_mean_head.txt"), rt_head) 27 | 28 | 29 | # rank is the actual core-number, size is total number of cores 30 | rank = MPI.COMM_WORLD.Get_rank() 31 | size = MPI.COMM_WORLD.Get_size() 32 | 33 | # state if OGS5 output files should be kept 34 | keep_output = False 35 | # size of the ensembles 36 | ens_size = 1000 37 | # pumping rate (1L / s) 38 | prate = -1e-4 39 | # parameter lists to generate the para_set (single one) 40 | TG = [1e-4] # mu = log(TG) 41 | var = [1.0, 2.25] 42 | len_scale = [10, 20] 43 | S = [1e-4] 44 | hurst = [0.5, 0.9] 45 | para_set = np.array( 46 | [[s, t, v, l, h] for t in TG for v in var for l in len_scale for s in S for h in hurst] 47 | ) 48 | 49 | RES = os.path.join("..", "..", "results") 50 | # ogs configuration 51 | task_root = os.path.abspath(os.path.join(RES, "eGRF_TPL_2D")) 52 | pcs_type_flow = "GROUNDWATER_FLOW" 53 | var_name_flow = "HEAD" 54 | 55 | # generate a model for each core (prevent writing conflicts) 56 | cstr = "core{:04}".format(rank) 57 | model = OGS(task_root=os.path.join(task_root, cstr), task_id="model") 58 | 59 | # spatio-temporal configuration 60 | # define the time stepping: 2 h with 32 steps and increasing stepsize 61 | time = specialrange(0, 7200, 32, typ="cub") 62 | # radial discretization: 1000 m with 100 steps and increasing stepsize 63 | rad = specialrange(0, 1000, 100, typ="cub") 64 | # 64 angles for discretization 65 | angles = 64 66 | 67 | # generate mesh and gli 68 | model.msh.generate("radial", dim=2, angles=angles, rad=rad) 69 | model.gli.generate("radial", dim=2, angles=angles, rad_out=rad[-1]) 70 | # add the pumping well 71 | model.gli.add_points(points=[0.0, 0.0, 0.0], names="pwell") 72 | 73 | # --------------generate different ogs input settings------------------------ # 74 | 75 | model.pcs.add_block( # set the process type 76 | PCS_TYPE=pcs_type_flow, NUM_TYPE="NEW" 77 | ) 78 | model.mpd.add(name="transmissivity") 79 | model.mpd.add_block( # edit recent mpd file 80 | MSH_TYPE=pcs_type_flow, MMP_TYPE="PERMEABILITY", DIS_TYPE="ELEMENT", 81 | ) 82 | model.mmp.add_block( # permeability, storage and porosity 83 | GEOMETRY_DIMENSION=2, 84 | PERMEABILITY_TENSOR=["ISOTROPIC", 1.0], 85 | PERMEABILITY_DISTRIBUTION=model.mpd.file_name, 86 | ) 87 | model.bc.add_block( # set boundary condition 88 | PCS_TYPE=pcs_type_flow, 89 | PRIMARY_VARIABLE=var_name_flow, 90 | GEO_TYPE=["POLYLINE", "boundary"], 91 | DIS_TYPE=["CONSTANT", 0.0], 92 | ) 93 | model.ic.add_block( # set the initial condition 94 | PCS_TYPE=pcs_type_flow, 95 | PRIMARY_VARIABLE=var_name_flow, 96 | GEO_TYPE="DOMAIN", 97 | DIS_TYPE=["CONSTANT", 0.0], 98 | ) 99 | model.st.add_block( # set pumping condition at the pumpingwell 100 | PCS_TYPE=pcs_type_flow, 101 | PRIMARY_VARIABLE=var_name_flow, 102 | GEO_TYPE=["POINT", "pwell"], 103 | DIS_TYPE=["CONSTANT_NEUMANN", prate], 104 | ) 105 | model.num.add_block( # set the parameters for the solver 106 | PCS_TYPE=pcs_type_flow, LINEAR_SOLVER=[2, 5, 1.0e-14, 1000, 1.0, 100, 4], 107 | ) 108 | model.tim.add_block( # set the TIMESTEPS 109 | PCS_TYPE=pcs_type_flow, **generate_time(time) 110 | ) 111 | model.out.add_block( # set the outputformat for the whole domain 112 | PCS_TYPE=pcs_type_flow, 113 | NOD_VALUES=var_name_flow, 114 | GEO_TYPE="DOMAIN", 115 | DAT_TYPE="PVD", 116 | TIM_TYPE=["STEPS", 1], 117 | ) 118 | 119 | # --------------run OGS simulation------------------------------------------- # 120 | 121 | print("write files on core {:02}".format(rank)) 122 | model.write_input() 123 | 124 | # save meta info only on core 0 125 | if rank == 0: 126 | np.savetxt(os.path.join(task_root, "time.txt"), time) 127 | np.savetxt(os.path.join(task_root, "rad.txt"), rad) 128 | np.savetxt(os.path.join(task_root, "angles.txt"), [angles]) 129 | # collect failed runs 130 | FAIL = [] 131 | # use a rank dependently seeded pseudo-random number generator 132 | seed = gs.random.MasterRNG(rank) 133 | for para_no, para in enumerate(para_set): 134 | if rank == 0: 135 | print("PARA_SET {:04}".format(para_no)) 136 | # set storativity 137 | model.mmp.update_block(STORAGE=[1, para[0]]) 138 | model.mmp.write_file() 139 | # init cov model (truncated power law with gaussian modes) 140 | cov = gs.TPLGaussian(dim=2, var=para[2], len_scale=para[3], hurst=para[4]) 141 | # init spatial random field class 142 | srf = gs.SRF(cov, mean=np.log(para[1]), upscaling="coarse_graining") 143 | # run the ensemble 144 | for i in range(ens_size): 145 | # parallel running the right jobs on each core 146 | if (para_no * ens_size + i) % size != rank: 147 | continue 148 | # generate new transmissivity field 149 | srf.mesh(model.msh, seed=seed(), point_volumes=model.msh.volumes_flat) 150 | # transfrom to log-normal field 151 | tf.normal_to_lognormal(srf) 152 | # add the transmissivity to the ogs project 153 | model.mpd.update_block(DATA=by_id(srf.field)) 154 | # write the new mpd file 155 | model.mpd.write_file() 156 | # set the new output-directory 157 | model.output_dir = os.path.join( 158 | task_root, "para{:04}".format(para_no), "seed{:04}".format(i) 159 | ) 160 | print(" run model {:04}".format(i), end=" ") 161 | success = model.run_model(print_log=False, save_log=keep_output) 162 | print(" ...success") if success else print(" ...error!") 163 | if not success: 164 | FAIL.append(str(para_no) + "_" + str(i)) 165 | # calculate angular means 166 | angles_mean(time, rad, angles, model.output_dir) 167 | # export the generated transmissivity field as vtk 168 | if keep_output: 169 | model.msh.export_mesh( 170 | os.path.join(model.output_dir, "field.vtu"), 171 | file_format="vtk", 172 | cell_data_by_id={"transmissivity": srf.field}, 173 | ) 174 | else: 175 | files = model.output_files(pcs="GROUNDWATER_FLOW", typ="PVD") 176 | files.append("model_GROUNDWATER_FLOW.pvd") 177 | for file in files: 178 | os.remove(os.path.join(model.output_dir, file)) 179 | if rank == 0: 180 | np.savetxt( # save current parameter set to file 181 | os.path.join(task_root, "para{:04}".format(para_no), "para.txt"), 182 | para, 183 | header="storage, trans_gmean, var, len_scale, hurst", 184 | ) 185 | # remove OGS5 settings 186 | if not keep_output: 187 | shutil.rmtree(os.path.join(task_root, cstr)) 188 | # final success message 189 | if FAIL: 190 | print("core {:02} FAILED:".format(rank), FAIL) 191 | else: 192 | print("core {:02} SUCCESS".format(rank)) 193 | -------------------------------------------------------------------------------- /results/eGRF_TPL_2D/para0005/rad_mean_head.txt: 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