The statistic zsalt can be viewed as the root mean

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Unformatted text preview: alysis of salt wedge via Φ-transform It is clear from both Fig. 4 (mean ZSALT) and Fig. 5 (random ZSALT) that the interface elevation ZSALT(x,y) follows a nonlinear trend along x (for fixed y) and cannot be a stationary random function of x. This observation has two consequences: 1. Given a single replicate of the coastal aquifer in (x,y), we can only sample in the shorewise direction (y) to produce a statistical description of the salt wedge. 2. For theoretical purposes, we may seek a convenient transformation ZSALT → Φ to obtain an approximate stationary field Φ from the non-stationary field ZSALT. 6.1 Transformation of ZSALT into a potential Φ Following this idea, consider first the analytical solution of the homogenous problem (σ = 0) using the Badon-Ghyben-Herzberg assumption, modified to include a submarine outflow face of height ΔZ at the seashore : ⎛ ε ΔZ ⎞ Z SALT ( x ) = Z SEA − ⎜ ⎟ − ΔZ − ⎝ ε +1 ⎠ 2 x H 12 − Z SEA (ε + 1) ⎛ ε Δ Z ⎞ +⎜ ⎟ ε LX ε (ε + 1) ⎝ ε +1...
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