Analyzing input and structural uncertainty of nonlinear dynamic models with stochastic, time-dependent parameters

A recently developed technique for identifying continuous-time, time-dependent, stochastic model parameters is embedded in a general framework for identifying causes of bias and reducing bias in dynamic models. In contrast to the usual approach of considering bias in model output with an autoregressive error model or a stochastic process, we make the attempt to correct for bias within the model or even in model input. This increases the potential of learning about the causes of bias and of subsequently correcting deficits of the deterministic model structure. The time-dependent parameters as formulated in our approach can also consistently be used for adding stochasticity to the model without losing precise fulfilment of conservation laws used for deriving the model equations. An additional advantage of the suggested procedure is that it makes it possible to derive more realistic uncertainty bounds of internal model variables than is the case when bias is only considered for measured model output. This is important for mechanistic models in which internal variables have a direct physical meaning. The concept is illustrated by an application to a simple eight-parameter conceptual hydrological model. This application demonstrates the feasibility of the proposed approach and gives an impression of its potential for application to a large class of nonlinear, dynamic models.