Throughout the world, watershed modeling is undertaken using lumped parameter
hydrologic models that represent real-world processes in a manner that is at once abstract,
but nevertheless relies on algorithms that reflect real-world processes and parameters that
reflect real-world hydraulic properties. In most cases, values are assigned to the
parameters of such models through calibration against flows at watershed outlets. One
criterion by which the utility of the model and the success of the calibration process
are judged is that realistic values are assigned to parameters through this process. This
study employs regularization theory to examine the relationship between lumped
parameters and corresponding real-world hydraulic properties. It demonstrates that
any kind of parameter lumping or averaging can induce a substantial amount of ‘structural
noise’ which devices such as Box-Cox transformation of flows and auto-regressive
moving average (ARMA) modeling of residuals are unlikely to render homoscedastic
and uncorrelated. Furthermore, values estimated for lumped parameters are unlikely to
represent average values of the hydraulic properties after which they are named and
are often contaminated to a greater or lesser degree by the values of hydraulic properties
which they do not purport to represent at all. As a result, the question of how rigidly
they should be bounded during the parameter estimation process is still an open one