The use of dynamic mathematical models to simulate the behaviour of environmental systems is common practice. However, the output of these models remains uncertain, despite their widespread use and long history of application. This uncertainty arises, amongst other factors, from errors in the data, randomness in natural processes, incorrect assumptions in the model structure with respect to the processes taking place in the natural system, and the inability of calibration procedures to unambiguously identify an optimal parameter set to represent the system under investigation. The latter two problems may be caused by the inability of the calibration procedure to retrieve sufficient information from the model residuals. In this paper, a new approach called Dynamic Identifiability Analysis is presented in order to partly overcome this limitation. A case study shows how the proposed methodology can be applied to increase the identifiability of parameters of a river solute transport model.

Abstract. The relationship between the distributed transient storage (TS) and lumped aggregate dead zone (ADZ) models of longitudinal solute transport in rivers and streams is examined by a parallel application to tracer data and through an investigation of parameter relationships. Both models accurately describe observed solute transport in a stream where the effects of storage or dead zones significantly affect longitudinal dispersion. A moment matching technique, based on theoretical temporal moments, is used to develop parameter relationships. Tests using the previously calibrated parameters, in addition to simulation experiments, show that the moment matching procedure allows ADZ model parameters to be reliably derived from TS model parameters and vice versa. An investigation of these parameter relationships reveals an important difference between the effective solute transport velocity and the average reach flow velocity in streams subject to transient storage or dead zone processes. A number of practical uses for the derived relationships are suggested, including the ability to utilize powerful methods of system identification in the estimation of TS model parameters.

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Abstract. A modification to the well-known water quality model "Quality Simulation Along River Systems" (QUASAR) is presented, extending its utility to real-time forecasting applications such as the management and control of pollution incidents. Two aggregated dead-zone (ADZ) parameters, namely time delay and dispersive fraction, are incorporated into the existing model formulation, extending the current continuously stirred tank reactor based model processes to account for advective and active mixing volume dispersive processes. The resulting river water quality model combines the strengths of the QUASAR model, which has proven non-conservative pollutant modelling capabilities, with the accurate advection and dispersion characterisation of the ADZ model. A discrete-time mathematical representation of the governing equations is developed that enables efficient system identification methods of parameter estimation to be utilised. The enhanced water quality model and associated methods of parameter estimation are validated using data from tracer experiments conducted on the River Mimram. The revised model produces accurate predictions of observed concentration-time curves for conservative substances.

The first step in developing travel time and water quality models in streams is to correctly model solute transport mechanisms. In this paper a comparison between two solute transport models is performed. The parameters of the Transient Storage model (TS) and the Aggregated Dead Zone model (ADZ) are estimated using data of thirty seven tracer experiments carried out under different discharges in five mountain streams of Colombian Los Andes. Calibration is performed with the generalized uncertainty estimation method (GLUE) based on Monte-Carlo simulations. Aspects of model parameters identifiability and model parsimony are analyzed and discussed. The TS model with four parameters shows excellent results during calibration but the model parameters present high interaction and poor identifiability. The ADZ model with two independent and clearly identifiable parameters gives sufficiently precise calibration results. As a conclusion, it is stated that the ADZ model with only two parameters is a parsimonious model that is able to represent solute transport mechanisms of advection and longitudinal dispersion in the studied mountain streams. A simple model parameter estimation methodology as a function of discharge is proposed in this work to be used in prediction mode of travel time and solute transport applications along mountain streams.