While I am not an expert, I have worked with some people in hydrology. The traditional way to study hydrographs is to model responses as a linear time invariant system. Essentially, output signals like stream flow are related to input signals like precipitation. When precipitation increases, stream flow also increases, but there's a time delay. You can estimate this time delay deconvolving the signals. Essentially, we imagine precipitation as a signal \$$x : \mathbb{R} \to \mathbb{R}\$$ and stream flow as a signal \$$y : \mathbb{R} \to \mathbb{R}\$$ where stream flow is the convolution of \$$x\$$ and another function (called the impulse response, I think):

$y(t) = \int_{-\infty}^t f(\tau)x(t-\tau) d\tau$

Essentially, we suppose \$$y\$$ equals a linear combination of all past values of \$$x\$$, if you estimate \$$f\$$ you learn how the system responds to any input signal and you can estimate time delays and so on.

I think John was working on math for diagrams of linear time invariant systems somewhere, but I can't remember if it was in CASCADE or not.