Errors in Hydrological Variables and Their Effect on Model Parameters

We present a method to ascertain optimal parameter values in the presence of a known measurement error distribution. This method is known as simulation extrapolation (SIMEX). Say X is an input variable with no error and Y is the response variable. Consider instead of X our input variable is W where, W= X+ N(0, σ). The calibrated parameter with W as input is called the naïve parameter estimate. At the start of this method we generate a series of alternate realisations for W (denoted W*) by artificially adding white noise to W in increasing multiples of the error variance σ. Given the new estimate of the parameter (using realisations W*), it now becomes possible to speculate on what the parameter would be were it to have no additive noise (or an error variance of 0). The trend in altered parameter values provides a basis to extrapolate the parameters to a situation where no error exists.