Flow Regime-Dependent, Discharge Uncertainty Envelope for Uncertainty Analysis with Ensemble Methods

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A discharge uncertainty envelope is presented that provides an observation error model for data assimilation (DA) using discharge observations derived from measurement of stage using a rating curve. It uniquely represents the rating curve representation error, which is due to scale and process incompatibility between the rating curve hydrodynamic model and “true” discharge, within the observation error model. Ensemble methods, specifically, the iterative ensemble smoother (IES) algorithms in PEST++, provide the DA framework for this observation error model. The purpose of the uncertainty envelope is to describe prior observation uncertainty for ensemble methods of DA. Envelope implementation goals are (1) limiting the spread of the envelope to avoid conditioning to extreme parameter values and producing posterior parameter distributions with increased variance, and (2) incorporating a representative degree of observation uncertainty to avoid overfitting, which will introduce bias into posterior parameter estimates and predicted model outcomes. The expected uncertainty envelope is flow regime dependent and is delineated using stochastic, statistical methods before undertaking history matching with IES. Analysis of the goodness-of-fit between stochastically estimated “true” discharge and observed discharge provides criteria for the selection of best-fit parameter ensembles from IES results.