Dynamic identifiability analysis of the transient storage model for solute transport in rivers

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.

[1]  Soroosh Sorooshian,et al.  Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information , 1998 .

[2]  Brian J. Wagner,et al.  1 – Quantifying Hydrologic Interactions between Streams and Their Subsurface Hyporheic Zones , 2000 .

[3]  S. Chapra.  Surface Water-Quality Modeling , 1996 .

[4]  Sarah M. Dunn.  Imposing constraints on parameter values of a conceptual hydrological model using baseflow response , 1999 .

[5]  M. B. Beck,et al.  The Identifiability of Conceptual Hydrochemical Models , 1990 .

[6]  Franciscus Maria Kleissen.  Uncertainty and identifiability in conceptual models of surface water acidification , 1991 .

[7]  Vijay P. Singh,et al.  A toolkit for the development and application of parsimonious hydrological models. , 2002 .

[8]  Peter V Tryon,et al.  STARPAC :: the standards time series and regression package , 1987 .

[9]  R. Thomann,et al.  Principles of surface water quality modeling and control , 1987 .

[10]  Neil McIntyre,et al.  Towards reduced uncertainty in conceptual rainfall‐runoff modelling: dynamic identifiability analysis , 2003 .

[11]  Steven C. Chapra,et al.  On the relationship of transient storage and aggregated dead zone models of longitudinal solute transport in streams , 2000 .

[12]  Geoffrey Ingram Taylor,et al.  The dispersion of matter in turbulent flow through a pipe , 1954, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[13]  J. Nash,et al.  River flow forecasting through conceptual models part I — A discussion of principles☆ , 1970 .

[14]  M. B. Beck,et al.  The identification of conceptual hydrological models for surface water acidification , 1986 .

[15]  Hugo B. Fischer,et al.  Longitudinal Dispersion and Turbulent Mixing in Open-Channel Flow , 1973 .

[16]  Soroosh Sorooshian,et al.  Toward improved calibration of hydrologic models: Combining the strengths of manual and automatic methods , 2000 .

[17]  Robert L. Runkel,et al.  One-Dimensional Transport with Inflow and Storage (OTIS): A Solute Transport Model for Streams and Rivers , 1998 .

[18]  G. T. Orlob.  Mathematical Modeling of Water Quality: Streams, Lakes and Reservoirs , 1983 .

[19]  J. Harlin.  Development of a Process Oriented Calibration Scheme for the HBV Hydrological Model , 1991 .

[20]  Roy A. Walters,et al.  Simulation of solute transport in a mountain pool‐and‐riffle stream: A transient storage model , 1983 .

[21]  Brian J. Wagner,et al.  Experimental design for estimating parameters of rate‐limited mass transfer: Analysis of stream tracer studies , 1997 .

[22]  M. B. Beck,et al.  Identifying flow paths in models of surface water acidification , 1990 .

[23]  D. Legates,et al.  Evaluating the use of “goodness‐of‐fit” Measures in hydrologic and hydroclimatic model validation , 1999 .

[24]  G. Hornberger.  Eutrophication in peel inlet—I. The problem-defining behavior and a mathematical model for the phosphorus scenario , 1980 .

[25]  S. Mous,et al.  Identification of the movement of water in unsaturated soils: the problem of identifiability of the model , 1993 .

[26]  K. Beven,et al.  Progress and directions in rainfall-runoff modelling , 1993 .

[27]  A. P. Jackman,et al.  Transport and concentration controls for chloride, strontium, potassium and lead in Uvas Creek, a small cobble-bed stream in Santa Clara County, California, U.S.A.: 2. Mathematical modeling , 1984 .

[28]  Steven M. Gorelick,et al.  A Statistical Methodology for Estimating Transport Parameters: Theory and Applications to One‐Dimensional Advectivec‐Dispersive Systems , 1986 .

[29]  Keith Beven,et al.  The future of distributed models: model calibration and uncertainty prediction. , 1992 .

[30]  John E. Dennis,et al.  An Adaptive Nonlinear Least-Squares Algorithm , 1977, TOMS.

[31]  Anders Wörman,et al.  Comparison of models for transient storage of solutes in small streams , 2000 .

[32]  R. Spear.  Eutrophication in peel inlet—II. Identification of critical uncertainties via generalized sensitivity analysis , 1980 .

[33]  Soroosh Sorooshian,et al.  A framework for development and application of hydrological models , 2001, Hydrology and Earth System Sciences.