mescla.uncertainty.propagation

Analytical error propagation for mixing fractions.

After Genereux, D. (1998), Quantifying uncertainty in tracer-based hydrograph separations, Water Resources Research 34(4), 915-919.

The lesson of these formulas is in the denominator: uncertainty scales with 1 / (C1 - C2). A tracer that separates the end-members by only a factor of two will never give tight fractions, however precise the laboratory. Choosing tracers with a wide contrast matters more than measuring them well.

Feed these the standard deviation that reflects the spatial and temporal variability of the end-member, not the laboratory’s repeatability. The latter is typically an order of magnitude too optimistic and yields indefensible intervals.

Functions

delta_method	First-order propagation through an arbitrary function, by finite differences.
genereux_sigma	Standard deviation of the two-component mixing fraction f1.
two_component_uncertainty	Two-component fractions with a confidence interval, as a DataFrame.