On the relationship between the reliability of parameter estimates and hydrologic time series data used in calibration

Typically, some of the parameters of conceptual hydrologic models are calibrated using limited hydrologic information, namely, input‐output time series data such as precipitation and streamflow. The first part of this paper examines the sources of stochasticity in these models and then explores the conditions under which parameter estimates are consistent when only input‐output hydrologic time series data are used in calibration. This complements other work done on the stability of parameter estimates. Because the conditions for consistency are stringent, two ways of redressing this situation and also improving the stability of parameter estimates are considered in the second part. Two levels of additional information are considered. The first considers the use of the first two moments of measurement errors to make large sample bias corrections. The second employs time series data corresponding to storage volumes such as groundwater and soil moisture to remove the source of inconsistency due to inferring erroneously unobserved storage volumes and to improve the stability of parameter estimates. Proper use of such information must exploit the interdependence in model equations arising from coupled model structure and correlated disturbances. It is suggested that generalized least squares offers a promising approach for efficiently exploiting all available time series information in model calibration. Finally, a simple hydrologic example is given to illustrate the relationship between estimator reliability and time series data used in calibration.