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Calibration of time-series models traditionally attempts to reduce the total model prediction error by changing parameters so that simulations match or closely resemble observations. However, a shortcoming of this approach is the assumption that the observational error in the forcing input and output response data is insignificant. In most practical applications this is not the case. In addition, inappropriate model structures may provide good results even though they are actually not suitable representations of the true system of interest. Consequently, calibrated parameters can account for error, resulting in misleading performance and underestimated uncertainty. It is clearly necessary to validate calibrated parameters based on whether they produce realistic errors. Is there a way to estimate the “true” uncertainty in time-series models? Typically, the errors of model simulations are examined as the difference between the simulation output and the corresponding measured values, commonly referred to as the residual error time-series. These residual error time-series encapsulate error from multiple sources, including error in the observed input and output data, and error due to model structure problems and/or poor parameterisation. Estimation of the uncertainty within each of the potential error sources is ideally informed a priori but this requires detailed knowledge of the measurements or estimation techniques. In the absence of such information, the residual error time-series can be separated into different source components using data-based techniques. However, this requires the assumption that the nature of the errors are distinct for each of the different components. This study describes and tests a simple method that estimates separately the forcing input error and the output response error in state-dependent models. A major assumption of the method is that errors in the input data produce autocorrelated errors in the output of state-dependent models. In this paper, the assumptions of the method are tested using a simple state-dependent model. The method is outlined and a proof of concept performed using controlled conditions.

Time-series model calibrations – influence and estimation of different error types