Accruing pumping rate

AnaFlow provides different representations for the pumping condition. One is an accruing pumping rate represented by the error function. This could be interpreted as that the water pump needs a certain time to reach its constant rate state.

import matplotlib.gridspec as gridspec
import numpy as np
from matplotlib import pyplot as plt
from scipy.special import erf

from anaflow import theis

time = np.geomspace(1, 600)
rad = [1, 5]

# Q(t) = Q * erf(t / a)
a = 120
lap_kwargs = {"cond": 4, "cond_kw": {"a": a}}

head1 = theis(
    time=time,
    rad=rad,
    storage=1e-4,
    transmissivity=1e-4,
    rate=-1e-4,
    lap_kwargs=lap_kwargs,
)
head2 = theis(
    time=time,
    rad=rad,
    storage=1e-4,
    transmissivity=1e-4,
    rate=-1e-4,
)
gs = gridspec.GridSpec(2, 1, height_ratios=[1, 3])
ax1 = plt.subplot(gs[0])
ax2 = plt.subplot(gs[1], sharex=ax1)

for i, step in enumerate(rad):
    ax2.plot(
        time,
        head1[:, i],
        color="C" + str(i),
        label="accruing Theis(r={})".format(step),
    )
    ax2.plot(
        time,
        head2[:, i],
        color="C" + str(i),
        label="constant Theis(r={})".format(step),
        linestyle="--",
    )
ax1.plot(time, 1e-4 * erf(time / a), label="accruing Q")
ax2.set_xlabel("t in [s]")
ax2.set_ylabel("h in [m]")
ax1.set_ylabel(r"|Q| in [$\frac{m^3}{s}$]")
ax1.legend()
ax2.legend()
plt.tight_layout()
plt.show()