An environmental engineer is interested in estimating the mixing that occurs between a stratified lake and an adjacent embayment (Figure). A conservative tracer is instantaneously mixed with the bay water, and then the tracer concentration is monitored over the ensuing period in all three segments. The values are

Using mass balance, the system can be modeled as the following simultaneous ODEs:

where Vi = volume of segment i, Q = flow, and Eij = diffusive mixing rate between segments i and j. Use the data and the differential equations to estimate the E’s if V₁ = 1 x 10⁷, V₂ = 8 x 10⁶, V₃ = 5 x 10⁶, and Q = 4 x 10⁶. Employ Euler’s method with a step size of 0.1 for your analyses.

02 4 6 16 20 12 C0 15 11 7 6. 2 3. 6. 4 26 16 10 4 3 C 100 48 Upper layer (1) Bay (3) Lower layer (2)