Contaminant release history identification in 2-D heterogeneous aquifers through a minimum relative entropy approach

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Table 1 Summary of the study cases and numerical results

Case	Hydraulic conductivity field	No. of monitoring points	Sampling times	No. of observations	Measurement error σ_R (mg/L)	nRMSE (%)		nRMSE (%)
						Released history		Observed/Estimated
						Expected function estimate		Expected function estimate
						Gaussian	Boxcar	Gaussian	Boxcar
H01	Homogeneous	20 (Fig. 1)	T = 300Δt	20	–	1.85	1.20	1.40	1.09
H01	Homogeneous	20 (Fig. 1)	T = 300Δt	20	10⁻³	2.20	1.34	1.52	1.16
H02	Homogeneous	2 (P1 and P2 of Fig. 1)	15 collected every 20Δt up to T	30	–	5.37	5.72	2.43	2.10
H02	Homogeneous	2 (P1 and P2 of Fig. 1)	15 collected every 20Δt up to T	30	10⁻³	6.12	7.01	3.42	2.95
HE1	Heterogeneous	20 (Fig. 3)	T = 300Δt	20	–	7.49	34.91	2.07	5.22
HE1	Heterogeneous	20 (Fig. 3)	T = 300Δt	20	10⁻³	9.06	38.72	4.38	6.71
HE2	Heterogeneous	2 (P3 and P4 of Fig. 3)	25 collected every 12Δt up to T	50	–	4.59	4.88	4.57	3.84
HE2	Heterogeneous	2 (P3 and P4 of Fig. 3)	25 collected every 12Δt up to T	50	10⁻³	4.78	5.34	4.87	4.30