Combined analysis of time-varying sensitivity and identifiability indices to diagnose the response of a complex environmental model

Sensitivity and identifiability analyses are common diagnostic tools to address over-parametrization in complex environmental models, but a combined application of the two analyses is rarely conducted. In this study, we performed a temporal global sensitivity analysis using the variance-based method of Sobol' and a temporal identifiability analysis of model parameters using the dynamic identifiability method (DYNIA). We discuss the relationship between the two analyses with a focus on parameter identification and output uncertainty reduction. The hydrological model HydroGeoSphere was used to simulate daily evapotranspiration, water content, and seepage at the lysimeter scale. We found that identifiability of a parameter does not necessarily reduce output uncertainty. It was also found that the information from the main and total effects (main Sobol' sensitivity indices) is required to allow uncertainty reduction in the model output. Overall, the study highlights the role of combined temporal diagnostic tools for improving our understanding of model behavior. Main and total effects are both required to identify the important parameters.Identifiability is necessary but not sufficient for uncertainty reduction.Soil moisture affects temporal variability of sensitivity and identifiability.Combined diagnostic tools improve our understanding of complex model behavior.

[1]  M. V. Genuchten,et al.  A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media , 1993 .

[2]  Erwin Zehe,et al.  Inferring model structural deficits by analyzing temporal dynamics of model performance and parameter sensitivity , 2011 .

[3]  B. Croke,et al.  Addressing ten questions about conceptual rainfall–runoff models with global sensitivity analyses in R , 2013 .

[4]  J. Rozemeijer,et al.  Integrated modeling of groundwater–surface water interactions in a tile‐drained agricultural field: The importance of directly measured flow route contributions , 2010 .

[5]  Roger Moussa,et al.  Implementation of an automatic calibration procedure for HYDROTEL based on prior OAT sensitivity and complementary identifiability analysis , 2014 .

[6]  H. L. Penman Natural evaporation from open water, bare soil and grass , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[7]  Indrajeet Chaubey,et al.  Sensitivity and identifiability of stream flow generation parameters of the SWAT model , 2010 .

[8]  Tomas Vitvar,et al.  Estimation of mean water residence times and runoff generation by180 measurements in a Pre-Alpine catchment (Rietholzbach, Eastern Switzerland) , 1997 .

[9]  Carolina Massmann,et al.  Analysis of the behavior of a rainfall-runoff model using three global sensitivity analysis methods evaluated at different temporal scales , 2012 .

[10]  Florian Pappenberger,et al.  Sensitivity analysis based on regional splits and regression trees (SARS-RT) , 2006, Environ. Model. Softw..

[11]  H. Künsch,et al.  Practical identifiability analysis of large environmental simulation models , 2001 .

[12]  Wolfgang Durner,et al.  Inverse Estimation of Soil Hydraulic and Root Distribution Parameters from Lysimeter Data , 2012 .

[13]  L. Shawn Matott,et al.  Evaluating uncertainty in integrated environmental models: A review of concepts and tools , 2009 .

[14]  C. B. Graham,et al.  Controls and Frequency of Preferential Flow Occurrence: A 175‐Event Analysis , 2011 .

[15]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[16]  Norbert Demuth,et al.  Tracerhydrologische Untersuchungen am Lysimeter Rietholzbach , 1993 .

[17]  Kristin Isaacs,et al.  Estimating Sobol sensitivity indices using correlations , 2012, Environ. Model. Softw..

[18]  Willy Bauwens,et al.  Sobol' sensitivity analysis of a complex environmental model , 2011, Environ. Model. Softw..

[19]  M. Ye,et al.  A fully coupled numerical modeling for regional unsaturated-saturated water flow , 2012 .

[20]  John Doherty,et al.  Two statistics for evaluating parameter identifiability and error reduction , 2009 .

[21]  Stefano Tarantola,et al.  Sensitivity analysis practices: Strategies for model-based inference , 2006, Reliab. Eng. Syst. Saf..

[22]  Francesca Pianosi,et al.  A Matlab toolbox for Global Sensitivity Analysis , 2015, Environ. Model. Softw..

[23]  I. Sobola,et al.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[24]  Florian Pappenberger,et al.  Multi-method global sensitivity analysis of flood inundation models. , 2008 .

[25]  Tomas Vitvar,et al.  Swiss prealpine Rietholzbach research catchment and lysimeter: 32 year time series and 2003 drought event , 2012 .

[26]  E. Sudicky,et al.  Simulating the multi-seasonal response of a large-scale watershed with a 3D physically-based hydrologic model , 2008 .

[27]  S. T. Gower,et al.  Worldwide Historical Estimates of Leaf Area Index, 1932-2000 , 2001 .

[28]  Marco Franchini,et al.  Physical interpretation and sensitivity analysis of the TOPMODEL , 1996 .

[29]  Thorsten Wagener,et al.  A new approach to visualizing time-varying sensitivity indices for environmental model diagnostics across evaluation time-scales , 2014, Environ. Model. Softw..

[30]  N. Fohrer,et al.  How to improve the representation of hydrological processes in SWAT for a lowland catchment – temporal analysis of parameter sensitivity and model performance , 2014 .

[31]  Francesca Pianosi,et al.  Understanding the time‐varying importance of different uncertainty sources in hydrological modelling using global sensitivity analysis , 2016 .

[32]  P. Reed,et al.  Sensitivity-guided reduction of parametric dimensionality for multi-objective calibration of watershed models , 2009 .

[33]  B. Croke,et al.  A review of foundational methods for checking the structural identifiability of models: Results for rainfall-runoff , 2015 .

[34]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[35]  Keith Beven,et al.  A manifesto for the equifinality thesis , 2006 .

[36]  Thorsten Wagener,et al.  Testing the realism of model structures to identify karst system processes using water quality and quantity signatures , 2013 .

[37]  K. Kristensen,et al.  A MODEL FOR ESTIMATING ACTUAL EVAPOTRANSPIRATION FROM POTENTIAL EVAPOTRANSPIRATION , 1975 .

[38]  Paola Annoni,et al.  Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index , 2010, Comput. Phys. Commun..

[39]  Soroosh Sorooshian,et al.  Sensitivity analysis of a land surface scheme using multicriteria methods , 1999 .

[40]  Willem J. de Lange,et al.  An operational, multi-scale, multi-model system for consensus-based, integrated water management and policy analysis: The Netherlands Hydrological Instrument , 2014, Environ. Model. Softw..

[41]  I. Sobol Uniformly distributed sequences with an additional uniform property , 1976 .

[42]  Thorsten Wagener,et al.  Identifiability of transient storage model parameters along a mountain stream , 2013 .

[43]  Y. Mualem A New Model for Predicting the Hydraulic Conductivity , 1976 .

[44]  Paul D. Bates,et al.  Distributed Sensitivity Analysis of Flood Inundation Model Calibration , 2005 .

[45]  William Castaings,et al.  Characterization of process-oriented hydrologic model behavior with temporal sensitivity analysis for flash floods in Mediterranean catchments , 2013 .

[46]  B. Mohanty,et al.  Uncertainty in dual permeability model parameters for structured soils , 2012, Water resources research.

[47]  Mario Schirmer,et al.  The effect of model complexity in simulating unsaturated zone flow processes on recharge estimation at varying time scales , 2015 .

[48]  Francesca Pianosi,et al.  Global Sensitivity Analysis of environmental models: Convergence and validation , 2016, Environ. Model. Softw..

[49]  Patrick M. Reed,et al.  Time‐varying sensitivity analysis clarifies the effects of watershed model formulation on model behavior , 2013 .

[50]  Patrick M. Reed,et al.  Multiobjective sensitivity analysis to understand the information content in streamflow observations for distributed watershed modeling , 2009 .

[51]  Fred L. Ogden,et al.  Sensitivity and uncertainty analysis of the conceptual HBV rainfall-runoff model: implications for parameter estimation. , 2010 .

[52]  Marnik Vanclooster,et al.  How efficient are one-dimensional models to reproduce the hydrodynamic behavior of structured soils subjected to multi-step outflow experiments? , 2010 .

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

[54]  Yuqiong Liu,et al.  Reconciling theory with observations: elements of a diagnostic approach to model evaluation , 2008 .

[55]  G. Fu,et al.  Sobol′’s sensitivity analysis for a distributed hydrological model of Yichun River Basin, China , 2013 .