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Measuring Hydraulic Properties Using a Line Source

I. Analytical Expressions

^a School of Geography and Geology, McMaster Univ., Hamilton, ON, Canada L8S 4M1
^b Dep. of Land Resource Science, Univ. of Guelph, Guelph, ON, Canada N1G 2W1
^c Graduate Studies and Research, Univ. of Saskatchewan, Rm 50 Murray Bldg, 3 Campus Drive, Saskatoon, SK, Canada S7N 5A4

View larger version (34K): [in a new window]   Fig. 1 Sensitivity coefficients, µ and µKs to 1% changes in and q/Ks. (a) and (b): for pressure head, (c) and (d): for water storage, and (e) and (f): for tracer travel time. Other parameters included: horizontal distance perpendicular to the source x = 0, L = 0.4 m, sk = 0.4, rk = 0.05, k = 12 m-1, Ksk = 2.8 x 10-5 m s-1, and q = 1 x 10-6 m2 s-1. Subscript k stands for the true value of the corresponding parameter

View larger version (51K): [in a new window]   Fig. 2 Spatial sensitivity of pressure head, water storage and tracer travel time solutions. (a) contours of µ in the x-z plane, (b) contours of µWKs in the x-z plane, (c) contours of µW in the x–plane, and (d) µT and µTKs vs. soil depth. Other parameters included: sk = 0.4, rk = 0.05, k = 12 m-1, Ksk = 2.8 x 10-5 m s-1, and q = 1 x 10-6 m2 s-1. Subscript k stands for the true value of the corresponding parameter

View larger version (54K): [in a new window]   Fig. 3 Response surfaces in the s-Ks plane obtained by using a single set of error-free measurements of (a) water storage, and (b) tracer travel time. Other parameters include: sk = 0.4, rk = 0.05, k = 12 m-1, Ksk = 2.8 x 10-5 m s-1, and q = 1 x 10-6 m2 s-1. Subscript k stands for the true value of the corresponding parameter

View larger version (31K): [in a new window]   Fig. 4 Response surfaces in the –Ks plane obtained by means of a single set of error-free measurements of (a) pressure head, (b) water storage, and (c) tracer travel time. Other parameters include: sk = 0.4, rk = 0.05, k = 12 m-1, Ksk = 2.8 x 10-5 m s-1, and q = 1 x 10-6 m2 s-1. Subscript k stands for the true value of the corresponding parameter

View larger version (26K): [in a new window]   Fig. 5 Response surfaces in the -Ks plane obtained by the two-set combination approaches: (a) +W, (b) +T, and (c) W+T. Other parameters include: sk = 0.4, rk = 0.05, k = 12 m-1, Ksk = 2.8 x 10-5 m s-1, and q = 1 x 10-6 m2 s-1. Subscript k stands for the true value of the corresponding parameter

View larger version (34K): [in a new window]   Fig. 6 Response surface in the -Ks plane obtained by the three-set combination approach. Other parameters include: sk = 0.4, rk = 0.05, k = 12 m-1, Ksk = 2.8 x 10-5 m s-1, and q = 1 x 10-6 m2 s-1. Subscript k stands for the true value of the corresponding parameter

View larger version (18K): [in a new window]   Fig. 7 Comparison of the exact solution and the approximate solution of travel time in a sandy soil. sk = 0.4, rk = 0.05, k = 12 m-1, Ksk = 2.8 x 10-5 m s-1, and q = 1 x 10-6 m2 s-1. Subscript k stands for the true value of the corresponding parameter

View larger version (14K): [in a new window]   Fig. 8 The relative error in the approximate solution calculated at different soil depths. Parameters: sk = 0.4, rk = 0.05, k = 12 m-1, Ksk = 2.8 x 10-5 m s-1, and q = 1 x 10-6 m2 s-1. Subscript k stands for the true value of the corresponding parameter