Correction to: Environmental Earth Sciences (2022) 81:185 https://doi.org/10.1007/s12665-022-10309-9

The original article has been published inadvertently with some errors in figures (Figs. 1, 2, 3, 4, 5, 6, 7, 8, 10, 12 and 13), in which some symbols and characters (“ = ”, “ × ”, “/”, “ ≥ ”, “ < ”, “¯”, “,” and “0”) were missing. All the corrected versions of figures are given below.

Fig. 1
figure 1

Illustration of a slug-injection tracer test. A slug of conservative tracer is instantaneously injected at x = 0 into a system governed by one-dimensional uniform flow along the x-axis

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Fig. 2
figure 2

Spatial concentration distributions of the solute plume at various travel distances (\(\overline{x}\) = 1.0 × 100, 1.0 × 101, 4.0 × 101, 1.0 × 102) according to Eq. (1)

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Fig. 3
figure 3

Truncated concentration distributions of the solute plume at various travel distances (\(\overline{x}\) = 1.0 × 100, 1.0 × 101, 4.0 × 101, 1.0 × 102) for the detection limit Clim/C0 = 2.0 × 10−2 (dash line)

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Fig. 4
figure 4

Two-dimensional concentration maps of a tracer slug at various travel distances according to Eq. (3): a \(\overline{x}_{1}\)  = 1.0 × 100, b \(\overline{x}_{1}\)  = 1.0 × 101, c \(\overline{x}_{1}\)  = 4.0 × 101, and d \(\overline{x}_{1}\)  = 1.0 × 102

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Fig. 5
figure 5

Two-dimensional concentration maps of a tracer slug truncated by the detection limit Clim/C0 = 2.0 × 10−3 at various travel distances: a \(\overline{x}_{1}\)  = 1.0 × 100, b \(\overline{x}_{1}\)  = 1.0 × 101, c \(\overline{x}_{1}\)  = 4.0 × 101, and d \(\overline{x}_{1}\)  = 1.0 × 102

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Fig. 6
figure 6

Dimensionless measured total mass and transport parameters for the one-dimensional case calculated at several travel distances (\(\overline{x}\) = 100, 101, 102) as a function of the dimensionless detection limit: a measured total mass, b longitudinal dispersivity, and c pore velocity

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Fig. 7
figure 7

Dimensionless measured total mass and transport parameters for the two-dimensional case calculated at several travel distances (\(\overline{x}_{1}\)  = 100, 101, 102) as a function of the dimensionless detection limit: a measured total mass, b longitudinal dispersivity, c transverse dispersivity, and d pore velocity

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Fig. 8
figure 8

Relative error ε of the longitudinal dispersivity as a function of the average travel distance and detection limit for the one- and two-dimensional cases: a one-dimensional case, b two-dimensional case (\({{\alpha_{T} } \mathord{\left/ {\vphantom {{\alpha_{T} } {\alpha_{L} }}} \right. \kern-\nulldelimiterspace} {\alpha_{L} }} = 0.1\)), and c two-dimensional case (\({{\alpha_{T} } \mathord{\left/ {\vphantom {{\alpha_{T} } {\alpha_{L} }}} \right. \kern-\nulldelimiterspace} {\alpha_{L} }} = 0.5\))

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Fig. 10
figure 10

Image of the initial solute plume that exhibited a nearly circular shape with a radius of about 2 cm

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Fig. 12
figure 12

Observed concentration maps at several times in the experiment: a Clim/C0 = 0; b Clim/C0 = 1.5 × 10 − 1

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Fig. 13
figure 13

Parameters observed at different travel distances (\(\overline{x}\) = 56, 98 cm) as a function of the dimensionless detection limit: a measured total mass, b longitudinal dispersivity, c transverse dispersivity, and d pore velocity. The symbols represent the average value of three experimentally estimated parameters. The vertical bars correspond to maximal and minimal values. The lines denote the values estimated from the analytical solution

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