add comparison of tpl-gaussian and matern models

Author: MuellerSeb

README.md

@@ -31,6 +31,8 @@ The workflow is organized by the following structure:
   - `03_literature_transmissivities.py` - comparision of drawdowns for different
     transimissivites from literature
   - `04_trans_plot.py` - plot a realization of a TPL transmissivity field
+  - `05_KTPL_plot.py` - plot K_TPL for different dimensions
+  - `06_tplgaussian_vs_matern.py` - comparison of TPL-Gaussian and Matern models
   - `comparison/` - scripts for the comparison of ensemble mean to effective TPL heads
     - `00_run_sim_mpi.sh` - bash file running `01_run_sim.py` in parallel
     - `01_run_sim.py` - run all ensemble simulations for pumping tests on TPL aquifers
@@ -43,7 +45,7 @@ The workflow is organized by the following structure:
 Main Python dependencies are stored in `requirements.txt`:
 
 ```
-gstools==1.2.1
+gstools==1.3.0
 anaflow==1.0.1
 ogs5py==1.1.1
 matplotlib

requirements.txt

@@ -1,4 +1,4 @@
-gstools==1.2.1
+gstools==1.3.0
 anaflow==1.0.1
 ogs5py==1.1.1
 matplotlib

results/06_matern_tpl_1-5.pdf

@@ -0,0 +1,151 @@
+"""TPL-Gaussian model vs. Matern model family."""
+import os
+import numpy as np
+import matplotlib as mpl
+from matplotlib import pyplot as plt
+import gstools as gs
+
+plt.style.use("default")
+mpl.rc("text", usetex=True)
+mpl.rc("lines", linewidth=3.5)
+plt.close("all")
+
+
+def dashes(i=1, max_d=12, space=1):
+    """Dashes for matplotlib."""
+    return i * [space, space] + [max_d - 2 * i * space, space]
+
+
+def format_ax(axis):
+    """Format axis."""
+    axis.set_xlim([-0.06, 3.06])
+    axis.set_xticks(range(4))
+    axis.set_xticklabels(["$0$", r"$\ell$", r"$2\ell$", r"$3\ell$"])
+    axis.set_xlabel("distance")
+    axis.set_ylabel("semivariance")
+    axis.set_ylim([0, 1])
+    axis.grid(linestyle=":")
+    axis.legend()
+
+
+save = True
+x = np.geomspace(0.01, 3, 10)
+grid = np.linspace(0, 10, 100)
+
+# Matern(nu=1.5) vs TPL-Gaussian
+
+fig, ax = plt.subplots(figsize=[5, 3])
+
+m1 = gs.Matern(dim=2, integral_scale=1, nu=1.5)
+fit_m1 = gs.TPLGaussian(dim=2)
+fit_m1.fit_variogram(x, m1.variogram(x), len_low=0, nugget=0)
+m1.plot(ax=ax, x_max=3, label="Matern(nu=1.5)", color="k", linewidth=2)
+fit_m1.plot(
+    ax=ax, x_max=3, label="TPL-Gaussian(hurst=1.0)", linestyle=":", color="C0"
+)
+
+print(m1)
+print(fit_m1)
+
+format_ax(ax)
+fig.tight_layout()
+if save:
+    fig.savefig(
+        os.path.join("..", "results", "06_matern_tpl_1-5.pdf"), dpi=300
+    )
+    fig.show()
+
+# Matern(nu=0.5) vs TPL-Gaussian
+
+fig, ax = plt.subplots(figsize=[5, 3])
+
+m2 = gs.Matern(dim=2, integral_scale=1, nu=0.5)
+fit_m2 = gs.TPLGaussian(dim=2)
+fit_m2.fit_variogram(x, m2.variogram(x), len_low=0, nugget=0)
+m2.plot(ax=ax, x_max=3, label="Matern(nu=0.5)", color="k", linewidth=2)
+fit_m2.plot(
+    ax=ax, x_max=3, label="TPL-Gaussian(hurst=0.45)", linestyle=":", color="C0"
+)
+
+print(m2)
+print(fit_m2)
+
+format_ax(ax)
+fig.tight_layout()
+if save:
+    fig.savefig(
+        os.path.join("..", "results", "07_matern_tpl_0-5.pdf"), dpi=300
+    )
+    fig.show()
+
+# model families
+
+fig, ax = plt.subplots(figsize=[5, 3])
+
+gau = gs.Gaussian(integral_scale=1)
+exp = gs.Exponential(integral_scale=1)
+nus = [0.5, 0.75, 1.0, 1.5, 2.0]
+# ax = exp.plot(ax=ax, x_max=3, linestyle="-.", color="k")
+ax = gau.plot(ax=ax, x_max=3, linestyle="-", color="k")
+for i, nu in enumerate(nus):
+    m = gs.Matern(integral_scale=1, nu=nu)
+    ax = m.plot(
+        ax=ax,
+        x_max=3,
+        label=f"Matern(nu={nu:.2})",
+        linewidth=2,
+        dashes=dashes(i),
+        color="C0",
+    )
+format_ax(ax)
+fig.tight_layout()
+if save:
+    fig.savefig(os.path.join("..", "results", "08_matern_family.pdf"), dpi=300)
+fig.show()
+
+fig, ax = plt.subplots(figsize=[5, 3])
+
+hursts = [0.45, 0.5, 0.6, 0.8, 0.999]
+# ax = exp.plot(ax=ax, x_max=3, linestyle="-.", color="k")
+ax = gau.plot(ax=ax, x_max=3, linestyle="-", color="k")
+for i, hurst in enumerate(hursts):
+    m = gs.TPLGaussian(integral_scale=1, hurst=hurst)
+    ax = m.plot(
+        ax=ax,
+        x_max=3,
+        label=f"TPL-Gaussian(hurst={hurst:.2})",
+        linewidth=2,
+        dashes=dashes(i),
+        color="C0",
+    )
+format_ax(ax)
+fig.tight_layout()
+if save:
+    fig.savefig(os.path.join("..", "results", "09_tpl_family.pdf"), dpi=300)
+fig.show()
+
+# Fields
+
+fig, ax = plt.subplots(figsize=[5, 4])
+srf = gs.SRF(m1, seed=1234)
+field1a = srf.structured((grid, grid))
+srf.plot(ax=ax, contour_plot=False)
+ax.set_title("Matern(nu=1.5)")
+fig.tight_layout()
+if save:
+    fig.savefig(
+        os.path.join("..", "results", "10_field_matern_1-5.pdf"), dpi=300
+    )
+fig.show()
+
+fig, ax = plt.subplots(figsize=[5, 4])
+srf = gs.SRF(m2, seed=1234)
+srf.structured((grid, grid))
+srf.plot(ax=ax, contour_plot=False)
+ax.set_title("Matern(nu=0.5)")
+fig.tight_layout()
+if save:
+    fig.savefig(
+        os.path.join("..", "results", "11_field_matern_0-5.pdf"), dpi=300
+    )
+fig.show()