Update DOC, examples and README

README.md

@@ -42,7 +42,7 @@ from anaflow import theis
 time = [10, 100, 1000]
 rad = np.geomspace(0.1, 10)
 
-head = theis(time=time, rad=rad, T=1e-4, S=1e-4, Qw=-1e-4)
+head = theis(time=time, rad=rad, transmissivity=1e-4, storage=1e-4, rate=-1e-4)
 
 for i, step in enumerate(time):
     plt.plot(rad, head[i], label="Theis(t={})".format(step))
@@ -60,27 +60,26 @@ plt.show()
 
 The following functions are provided directly
 
-```python
-anaflow.thiem        # Thiem solution for steady state pumping
-anaflow.theis        # Theis solution for transient pumping
-anaflow.ext_thiem2D  # extended Thiem solution in 2D
-anaflow.ext_theis2D  # extended Theis solution in 2D
-anaflow.ext_thiem3D  # extended Thiem solution in 3D
-anaflow.ext_theis3D  # extended Theis solution in 3D
-anaflow.grf_model    # "General Radial Flow" Model
-anaflow.grf_dist     # extended "General Radial Flow" Model on disks
-```
+* ``thiem`` Thiem solution for steady state pumping
+* ``theis`` Theis solution for transient pumping
+* ``ext_thiem_2d`` extended Thiem solution in 2D from *Zech 2013*
+* ``ext_theis_2d`` extended Theis solution in 2D from *Mueller 2015*
+* ``ext_thiem_3d`` extended Thiem solution in 3D from *Zech 2013*
+* ``ext_theis_3d`` extended Theis solution in 3D from *Mueller 2015*
+* ``neuman2004`` transient solution from *Neuman 2004*
+* ``neuman2004_steady`` steady solution from *Neuman 2004*
+* ``grf`` "General Radial Flow" Model
+* ``ext_grf`` the transient extended GRF model
+* ``ext_grf_steady`` the steady extended GRF model
 
 
 ### Laplace Transformation
 
 We provide routines to calculate the laplace-transformation as well as the
 inverse laplace-transformation of a given function
 
-```python
-anaflow.get_lap      # Get the laplace transformation of a function
-anaflow.get_lap_inv  # Get the inverse laplace transformation of a function
-```
+* ``get_lap`` Get the laplace transformation of a function
+* ``get_lap_inv`` Get the inverse laplace transformation of a function
 
 
 ## Requirements

docs/source/index.rst

@@ -27,16 +27,17 @@ Provided Functions
 
 The following functions are provided directly
 
-.. code-block:: python
-
-    anaflow.thiem        # Thiem solution for steady state pumping
-    anaflow.theis        # Theis solution for transient pumping
-    anaflow.ext_thiem2D  # extended Thiem solution in 2D
-    anaflow.ext_theis2D  # extended Theis solution in 2D
-    anaflow.ext_thiem3D  # extended Thiem solution in 3D
-    anaflow.ext_theis3D  # extended Theis solution in 3D
-    anaflow.grf_model    # "General Radial Flow" Model
-    anaflow.grf_dist     # extended "General Radial Flow" Model on disks
+* ``thiem`` Thiem solution for steady state pumping
+* ``theis`` Theis solution for transient pumping
+* ``ext_thiem_2d`` extended Thiem solution in 2D from *Zech 2013*
+* ``ext_theis_2d`` extended Theis solution in 2D from *Mueller 2015*
+* ``ext_thiem_3d`` extended Thiem solution in 3D from *Zech 2013*
+* ``ext_theis_3d`` extended Theis solution in 3D from *Mueller 2015*
+* ``neuman2004`` transient solution from *Neuman 2004*
+* ``neuman2004_steady`` steady solution from *Neuman 2004*
+* ``grf`` "General Radial Flow" Model
+* ``ext_grf`` the transient extended GRF model
+* ``ext_grf_steady`` the steady extended GRF model
 
 
 Laplace Transformation
@@ -45,10 +46,8 @@ Laplace Transformation
 We provide routines to calculate the laplace-transformation as well as the
 inverse laplace-transformation of a given function
 
-.. code-block:: python
-
-    anaflow.get_lap      # Get the laplace transformation of a function
-    anaflow.get_lap_inv  # Get the inverse laplace transformation of a function
+* ``get_lap`` Get the laplace transformation of a function
+* ``get_lap_inv`` Get the inverse laplace transformation of a function
 
 
 Requirements

docs/source/tutorial_01_call.rst

@@ -15,7 +15,7 @@ different time-steps.
     time = [10, 100, 1000]
     rad = np.geomspace(0.1, 10)
 
-    head = theis(time=time, rad=rad, T=1e-4, S=1e-4, Qw=-1e-4)
+    head = theis(time=time, rad=rad, transmissivity=1e-4, storage=1e-4, rate=-1e-4)
 
     for i, step in enumerate(time):
         plt.plot(rad, head[i], label="Theis(t={})".format(step))

docs/source/tutorial_02_extended_theis.rst

@@ -13,36 +13,42 @@ transmissivity.
 
     import numpy as np
     from matplotlib import pyplot as plt
-    from anaflow import theis, ext_theis2D
-
-
-    time = [10, 600, 36000]      # 10s, 10min, 10h
-    rad = np.geomspace(0.05, 4)  # radius from the pumping well in [0, 4]
-    var = 0.5                    # variance of the log-transmissivity
-    corr = 10.0                  # correlation length of the log-transmissivity
-    TG = 1e-4                    # the geometric mean of the transmissivity
-    TH = TG*np.exp(-var/2.0)     # the harmonic mean of the transmissivity
-    S = 1e-4                     # storativity
-    Qw = -1e-4                   # pumping rate
-
-    head_TG = theis(time=time, rad=rad, T=TG, S=S, Qw=Qw)
-    head_TH = theis(time=time, rad=rad, T=TH, S=S, Qw=Qw)
-    head_ef = ext_theis2D(time=time, rad=rad, TG=TG, sig2=var, corr=corr, S=S, Qw=Qw)
-
+    from anaflow import theis, ext_theis_2d
+
+
+    time_labels = ["10 s", "10 min", "10 h"]
+    time = [10, 600, 36000]       # 10s, 10min, 10h
+    rad = np.geomspace(0.05, 4)   # radius from the pumping well in [0, 4]
+    var = 0.5                     # variance of the log-transmissivity
+    len_scale = 10.0              # correlation length of the log-transmissivity
+    TG = 1e-4                     # the geometric mean of the transmissivity
+    TH = TG * np.exp(-var / 2.0)  # the harmonic mean of the transmissivity
+    S = 1e-4                      # storativity
+    rate = -1e-4                    # pumping rate
+
+    head_TG = theis(time, rad, S, TG, rate)
+    head_TH = theis(time, rad, S, TH, rate)
+    head_ef = ext_theis_2d(time, rad, S, TG, var, len_scale, rate)
+    time_ticks=[]
     for i, step in enumerate(time):
-        if i == 0:
-            label_TG = "Theis($T_G$)"
-            label_TH = "Theis($T_H$)"
-            label_ef = "extended Theis"
-        else:
-            label_TG = label_TH = label_ef = None
+        label_TG = "Theis($T_G$)" if i == 0 else None
+        label_TH = "Theis($T_H$)" if i == 0 else None
+        label_ef = "extended Theis" if i == 0 else None
         plt.plot(rad, head_TG[i], label=label_TG, color="C"+str(i), linestyle="--")
         plt.plot(rad, head_TH[i], label=label_TH, color="C"+str(i), linestyle=":")
         plt.plot(rad, head_ef[i], label=label_ef, color="C"+str(i))
+        time_ticks.append(head_ef[i][-1])
 
     plt.xlabel("r in [m]")
     plt.ylabel("h in [m]")
     plt.legend()
+    ylim = plt.gca().get_ylim()
+    plt.gca().set_xlim([0, rad[-1]])
+    ax2 = plt.gca().twinx()
+    ax2.set_yticks(time_ticks)
+    ax2.set_yticklabels(time_labels)
+    ax2.set_ylim(ylim)
+    plt.tight_layout()
     plt.show()
 
 

examples/01_call_theis.py

@@ -7,7 +7,7 @@
 time = [10, 100, 1000]
 rad = np.geomspace(0.1, 10)
 
-head = theis(time=time, rad=rad, T=1e-4, S=1e-4, Qw=-1e-4)
+head = theis(time=time, rad=rad, transmissivity=1e-4, storage=1e-4, rate=-1e-4)
 
 for i, step in enumerate(time):
     plt.plot(rad, head[i], label="Theis(t={})".format(step))

examples/02_call_ext_theis2d.py

@@ -1,22 +1,22 @@
 # -*- coding: utf-8 -*-
 import numpy as np
 from matplotlib import pyplot as plt
-from anaflow import theis, ext_theis2D
+from anaflow import theis, ext_theis_2d
 
 
 time_labels = ["10 s", "10 min", "10 h"]
-time = [10, 600, 36000]      # 10s, 10min, 10h
-rad = np.geomspace(0.05, 4)  # radius from the pumping well in [0, 4]
-var = 0.5                    # variance of the log-transmissivity
-corr = 10.0                  # correlation length of the log-transmissivity
-TG = 1e-4                    # the geometric mean of the transmissivity
-TH = TG*np.exp(-var/2.0)     # the harmonic mean of the transmissivity
-S = 1e-4                     # storativity
-Qw = -1e-4                   # pumping rate
+time = [10, 600, 36000]       # 10s, 10min, 10h
+rad = np.geomspace(0.05, 4)   # radius from the pumping well in [0, 4]
+var = 0.5                     # variance of the log-transmissivity
+len_scale = 10.0              # correlation length of the log-transmissivity
+TG = 1e-4                     # the geometric mean of the transmissivity
+TH = TG * np.exp(-var / 2.0)  # the harmonic mean of the transmissivity
+S = 1e-4                      # storativity
+rate = -1e-4                  # pumping rate
 
-head_TG = theis(time=time, rad=rad, T=TG, S=S, Qw=Qw)
-head_TH = theis(time=time, rad=rad, T=TH, S=S, Qw=Qw)
-head_ef = ext_theis2D(time=time, rad=rad, TG=TG, sig2=var, corr=corr, S=S, Qw=Qw)
+head_TG = theis(time, rad, S, TG, rate)
+head_TH = theis(time, rad, S, TH, rate)
+head_ef = ext_theis_2d(time, rad, S, TG, var, len_scale, rate)
 time_ticks=[]
 for i, step in enumerate(time):
     label_TG = "Theis($T_G$)" if i == 0 else None

examples/03_call_ext_theis3d.py

@@ -1,26 +1,26 @@
 # -*- coding: utf-8 -*-
 import numpy as np
 from matplotlib import pyplot as plt
-from anaflow import theis, ext_theis3D
+from anaflow import theis, ext_theis_3d
 from anaflow.tools.special import aniso
 
 
 time_labels = ["10 s", "10 min", "10 h"]
-time = [10, 600, 36000]                 # 10s, 10min, 10h
-rad = np.geomspace(0.05, 4)             # radial distance from the pumping well in [0, 4]
-var = 0.5                               # variance of the log-conductivity
-corr = 10.0                             # correlation length of the log-conductivity
-e = 0.75                                # anisotropy ratio of the log-conductivity
-KG = 1e-4                               # the geometric mean of the conductivity
-Kefu = KG*np.exp(var*(0.5 - aniso(e)))  # the effective conductivity for uniform flow
-KH = KG*np.exp(-var/2.0)                # the harmonic mean of the conductivity
-S = 1e-4                                # storage
-Qw = -1e-4                              # pumping rate
-L = 1.0                                 # vertical extend of the aquifer
+time = [10, 600, 36000]                  # 10s, 10min, 10h
+rad = np.geomspace(0.05, 4)              # radial distance from the pumping well in [0, 4]
+var = 0.5                                # variance of the log-conductivity
+len_scale = 10.0                         # correlation length of the log-conductivity
+anis = 0.75                              # anisotropy ratio of the log-conductivity
+KG = 1e-4                                # the geometric mean of the conductivity
+Kefu = KG*np.exp(var*(0.5-aniso(anis)))  # the effective conductivity for uniform flow
+KH = KG*np.exp(-var/2.0)                 # the harmonic mean of the conductivity
+S = 1e-4                                 # storage
+rate = -1e-4                             # pumping rate
+L = 1.0                                  # vertical extend of the aquifer
 
-head_Kefu = theis(time=time, rad=rad, T=Kefu*L, S=S, Qw=Qw)
-head_KH = theis(time=time, rad=rad, T=KH*L, S=S, Qw=Qw)
-head_ef = ext_theis3D(time=time, rad=rad, KG=KG, sig2=var, corr=corr, e=e, S=S, Qw=Qw, L=1)
+head_Kefu = theis(time, rad, S, Kefu*L, rate)
+head_KH = theis(time, rad, S, KH*L, rate)
+head_ef = ext_theis_3d(time, rad, S, KG, var, len_scale, anis, L, rate)
 time_ticks=[]
 for i, step in enumerate(time):
     label_TG = "Theis($K_{efu}$)" if i == 0 else None

examples/04_call_ext_theis_tpl.py

@@ -9,23 +9,23 @@
 rad = np.geomspace(0.05, 4)  # radial distance from the pumping well in [0, 4]
 S = 1e-4                     # storage
 KG = 1e-4                    # the geometric mean of the conductivity
-corr = 20.0                  # upper bound for the length scale
+len_scale = 20.0             # upper bound for the length scale
 hurst = 0.5                  # hurst coefficient
 var = 0.5                    # variance of the log-conductivity
-Qw = -1e-4                   # pumping rate
+rate = -1e-4                 # pumping rate
 KH = KG * np.exp(-var / 2)   # the harmonic mean of the conductivity
 
-head_KG = theis(time=time, rad=rad, T=KG, S=S, Qw=Qw)
-head_KH = theis(time=time, rad=rad, T=KH, S=S, Qw=Qw)
+head_KG = theis(time, rad, S, KG, rate)
+head_KH = theis(time, rad, S, KH, rate)
 head_ef = ext_theis_tpl(
     time=time,
     rad=rad,
-    S=S,
-    KG=KG,
-    corr=corr,
+    storage=S,
+    cond_gmean=KG,
+    len_scale=len_scale,
     hurst=hurst,
-    sig2=var,
-    Qw=Qw,
+    var=var,
+    rate=rate,
 )
 for i, step in enumerate(time):
     label_TG = "Theis($K_G$)" if i == 0 else None

examples/05_call_neuman2004.py

@@ -12,18 +12,18 @@
 TG = 1e-4                    # the geometric mean of the transmissivity
 TH = TG*np.exp(-var/2.0)     # the harmonic mean of the transmissivity
 S = 1e-4                     # storativity
-Qw = -1e-4                   # pumping rate
+rate = -1e-4                   # pumping rate
 
-head_TG = theis(time=time, rad=rad, T=TG, S=S, Qw=Qw)
-head_TH = theis(time=time, rad=rad, T=TH, S=S, Qw=Qw)
+head_TG = theis(time, rad, S, TG, rate)
+head_TH = theis(time, rad, S, TH, rate)
 head_ef = neuman2004(
     time=time,
     rad=rad,
     trans_gmean=TG,
     var=var,
     len_scale=len_scale,
     storage=S,
-    rate=Qw,
+    rate=rate,
 )
 time_ticks = []
 for i, step in enumerate(time):

examples/06_compare_extthiem2d_grfsteady.py

@@ -1,7 +1,7 @@
 # -*- coding: utf-8 -*-
 import numpy as np
 from matplotlib import pyplot as plt
-from anaflow import ext_thiem2D, grf_steady
+from anaflow import ext_thiem_2d, ext_grf_steady
 from anaflow.tools.coarse_graining import T_CG
 
 
@@ -12,8 +12,8 @@
 TG = 1e-4                    # the geometric mean of the transmissivity
 rate = -1e-4                 # pumping rate
 
-head1 = ext_thiem2D(rad, r_ref, TG, var, len_scale, rate)
-head2 = grf_steady(rad, r_ref, T_CG, rate=rate, TG=TG, sig2=var, corr=len_scale)
+head1 = ext_thiem_2d(rad, r_ref, TG, var, len_scale, rate)
+head2 = ext_grf_steady(rad, r_ref, T_CG, rate=rate, trans_gmean=TG, var=var, len_scale=len_scale)
 
 plt.plot(rad, head1, label="Ext Thiem 2D")
 plt.plot(rad, head2, label="grf(T_CG)", linestyle="--")

examples/07_compare_extthiem3d_grfsteady.py

@@ -1,7 +1,7 @@
 # -*- coding: utf-8 -*-
 import numpy as np
 from matplotlib import pyplot as plt
-from anaflow import ext_thiem3D, grf_steady
+from anaflow import ext_thiem_3d, ext_grf_steady
 from anaflow.tools.coarse_graining import K_CG
 
 
@@ -10,11 +10,11 @@
 var = 0.5                    # variance of the log-transmissivity
 len_scale = 10.0             # correlation length of the log-transmissivity
 KG = 1e-4                    # the geometric mean of the transmissivity
-e = 0.7                      # aniso ratio
+anis = 0.7                   # aniso ratio
 rate = -1e-4                 # pumping rate
 
-head1 = ext_thiem3D(rad, r_ref, KG, var, len_scale, e, rate, L=1)
-head2 = grf_steady(rad, r_ref, K_CG, rate=rate, KG=KG, sig2=var, corr=len_scale, e=e)
+head1 = ext_thiem_3d(rad, r_ref, KG, var, len_scale, anis, 1, rate)
+head2 = ext_grf_steady(rad, r_ref, K_CG, rate=rate, cond_gmean=KG, var=var, len_scale=len_scale, anis=anis)
 
 plt.plot(rad, head1, label="Ext Thiem 3D")
 plt.plot(rad, head2, label="grf(K_CG)", linestyle="--")

examples/08_compare_thiem_grfsteady.py

@@ -1,7 +1,7 @@
 # -*- coding: utf-8 -*-
 import numpy as np
 from matplotlib import pyplot as plt
-from anaflow import thiem, grf_steady
+from anaflow import thiem, ext_grf_steady
 
 
 rad = np.geomspace(0.05, 4)  # radius from the pumping well in [0, 4]
@@ -10,7 +10,7 @@
 rate = -1e-4                 # pumping rate
 
 head1 = thiem(rad, r_ref, T, rate)
-head2 = grf_steady(rad, r_ref, T, rate=rate)
+head2 = ext_grf_steady(rad, r_ref, T, rate=rate)
 
 plt.plot(rad, head1, label="Thiem")
 plt.plot(rad, head2, label="grf(T)", linestyle="--")

examples/09_compare_extthiem2d_neuman.py

@@ -1,7 +1,7 @@
 # -*- coding: utf-8 -*-
 import numpy as np
 from matplotlib import pyplot as plt
-from anaflow import ext_thiem2D, neuman2004_steady
+from anaflow import ext_thiem_2d, neuman2004_steady
 
 
 rad = np.geomspace(0.05, 4)  # radius from the pumping well in [0, 4]
@@ -11,7 +11,7 @@
 TG = 1e-4                    # the geometric mean of the transmissivity
 rate = -1e-4                 # pumping rate
 
-head1 = ext_thiem2D(rad, r_ref, TG, var, len_scale, rate)
+head1 = ext_thiem_2d(rad, r_ref, TG, var, len_scale, rate)
 head2 = neuman2004_steady(rad, r_ref, TG, var, len_scale, rate)
 
 plt.plot(rad, head1, label="extended Thiem 2D")