H14A-01 INVITED 16:00h
Interdisciplinary Knowledge Integration: Genuine Scientific Inquiry or 'Full-Bodied' Red Wine?
If the development of conceptual models is going to produce rigorous rules for the integration of knowledge from different disciplines and levels of organization, it should rely on an adequate understanding of scientific interdisciplinarity. Interdisciplinarity, however, is not always a clearly understood and widely accepted concept: (i) Interdisciplinarity has been viewed by certain groups in the same context as the unification of science, which refers to the pyramidal hierarchy that reduces one domain of science to another, seeking the unity of science and searching for the ultimate scientific truth. (ii) A distinction is made between interdisciplinarity producing a new discipline and interdisciplinarity involving the continuing interaction of a variety of disciplines without leading to a separate discipline. (iii) Another distinction is made between interdisciplinarity viewed as a merely practical activity happening on an everyday basis (e.g., studying the components of structured whole in isolation and applying ad hoc combinations to yield the final result) and interdisciplinarity considered for scientific research purposes (in which case issues of disciplinary incompleteness and non-reductive autonomy to be blended with another one may arise). In view of the above, genuinely interdisciplinary and innovative knowledge integration should not be confused with cosmetic inderdisciplinarity, the latter having a superficial and ad hoc interdisciplinary character allowing disciplinary business to go on as usual at the cheap price of some interdisciplinary rhetoric. In the cosmetic case 'interdisciplinarity' is used to describe -and praise- research projects as routinely as 'full-bodied' is used to describe red wines.
H14A-02 INVITED 16:15h
Parameter Uncertainty and Model Reliability in Groundwater modeling
Due to data limitation in both quantity and quality, a distributed parameter such as hydraulic conductivity must be approximated by a finite dimensional form when calibrating a conceptual groundwater model. This reduction in parameter dimension is known as parameterization and is necessary in order to obtain a stable and unique solution of the inverse problem. It has been pointed out by a number of researchers that in model calibration, one must consider simultaneously the parameter dimension, parameter pattern and parameter values. For a given set of observations, the least-squares error used for model calibration decreases when the parameter dimension increases. However, the parameter uncertainty error increases when over-parameterization occurs. The higher the parameter dimension, the more the required data. Over-parameterization occurs when information provided by the data is insufficient. Parameter uncertainty is usually represented by a norm of the covariance matrix of the estimated parameters. However, parameter uncertainty alone does not address the requirements of model application. To evaluate the model reliability in prediction, an additional criterion based on the error in model application must be considered. It is well understood that an over-simplified model structure may not be able to both fit the observed data and produce reliable predictions. On the other hand, a complex model structure may cause over-parameterization when data are limited. If a model is over-parameterized, the reliability of model prediction will decrease rather than increase. This paper reviews methods that have been developed to estimate the parameter uncertainty error as well as the model structure error when a simplified model structure is used to replace a more complex model structure.
H14A-03 INVITED 16:30h
Multi-model Ranking And Inference In Ground-Water Modeling
Uncertainty of hydrogeologic conditions makes it important to evaluate alternative plausible models in an effort to evaluate the character of a groundwater system, maintain parsimony, and make predictions with reasonable definition of their uncertainty. When multiple models are considered, data collection and analysis focuses on evaluation of which model(s) is(are) most supported by the data. Generally more than one model provides a similar acceptable fit to the observations, thus inference should be made from multiple models. Kullback-Leibler (K-L) information provides a rigorous foundation for model inference. Model evaluation based on K-L information is simple to compute, easy to interpret, and yields parsimonious models with more realistic measures of precision than evaluation of any one model, or evaluation based on other commonly referenced model selection criteria. Akaike's AICc, as modified by others after him, is a good tool for estimating K-L information. Alternative criteria such as: Bayesian information criterion (BIC of Schwarz), Hannan and Quinn's criterion (HQ), and Kashyap's criterion (KIC) have been suggested for selection of ground water models. Although use of these criteria for model ranking and multi-model inference produces similar results in practice: they strive to identify the best model; are based on the notion that full reality can be represented by a model exactly; and finally, assume that such a model is in the set of candidate models. This is in sharp contrast to the information-theoretic approach based on AICc where models are considered to be approximations to reality. In addition, as the number of observations increase, more details of the system can be uncovered, thus AICc selects more complex models. In contrast, BIC, HQ, and KIC seek the true model with consistent complexity regardless of the available number of observations. A computer-generated example illustrates the method.
H14A-04 16:45h
Hypothesis Testing by Model Rejection
Most applications of models in hydrology which make use of calibration against observations do not allow for model rejection but rather accept the optimal model as having value in prediction. The calibration process, including statistical methods of inference, is in fact generally carried out under the implicit assumption that the chosen model is correct. Only rarely are models, as competing hypotheses about how a system under study functions, compared within a framework that allows model rejection. Even rarer are studies reported that reject all the models tried when they show features in their response that do not match the available observations. This has perhaps been considered allowable because of the multiple sources of uncertainty in the modelling process. Even if the model might be correct, the forcing data used to drive it might be in error, the effective parameter values used might be in error, and the observations with which the model is compared might be in error. Thus model evaluation (and rejection) must take account of these different sources of uncertainty. This paper outlines a method for doing so as an extension of the GLUE methodology and demonstrates an application to rainfall-runoff modelling.
H14A-05 17:00h
A Framework for Dealing With Uncertainty due to Model Structure Error
Although uncertainty about structures of environmental models (conceptual uncertainty) has been recognised often to be the main source of uncertainty in model predictions, it is rarely considered in environmental modelling. Rather, formal uncertainty analyses have traditionally focused on model parameters and input data as the principal source of uncertainty in model predictions. The traditional approach to model uncertainty analysis that considers only a single conceptual model, fails to adequately sample the relevant space of plausible models. As such, it is prone to modelling bias and underestimation of model uncertainty. In this paper we review a range of strategies for assessing structural uncertainties. The existing strategies fall into two categories depending on whether field data are available for the variable of interest. Most research attention has until now been devoted to situations, where model structure uncertainties can be assessed directly on the basis of field data. This corresponds to a situation of `interpolation'. However, in many cases environmental models are used for `extrapolation' beyond the situation and the field data available for calibration. A framework is presented for assessing the predictive uncertainties of environmental models used for extrapolation. The key elements are the use of alternative conceptual models and assessment of their pedigree and the adequacy of the samples of conceptual models to represent the space of plausible models by expert elicitation. Keywords: model error, model structure, conceptual uncertainty, scenario analysis, pedigree
H14A-06 17:15h
Model Abstraction to Assess Uncertainty in Flow and Transport Modeling
Model abstraction (MA) is a methodology for reducing the complexity of a simulation model while maintaining the validity of the simulation results with respect to the question that the simulation is being used to address. The need for MA is recognized in simulations of complex systems where increased level of detail does not necessarily increase accuracy, but increases computational complexity, data collection burden, and difficulty to interpret results. We present a systematic classification and compendium of MA techniques for flow and transport modeling in soils. MA techniques were applied to soil water flow through a densely-instrumented soil profile of an experimental trench using: (a) Richards equation- and water budget-based models; (b) inverse modeling, laboratory measurements and pedotransfer functions to estimate parameters; (c) layered vs. homogeneous soil conceptual model. MA showed different efficiency when applied to soil water contents than to water fluxes. The water budget model was comparable to the mechanistic model with respect to water fluxes at coarse time scales. Measured hydraulic properties provided no advantage compared to pedotransfer functions. A spectrum of pedotransfer functions characterized uncertainty in hydraulic properties. One MA technique used neural networks to mimic simulated soil water flow. The MA application was useful both in understanding the flow system, and in justifying simplifications of its conceptualization and characterization.
H14A-07 INVITED 17:30h
Incorporating observational uncertainties more explicitly within GLUE: Examples using the rainfall-runoff model Dynamic TOPMODEL including predictions of fuzzy water table levels
The Generalised Likelihood Uncertainty Estimation (GLUE) procedure is underpinned by the equifinality thesis. This thesis maintains that for a given modelling problem, errors associated with the model structure and the observational data result in multiple acceptable representations that cannot be easily rejected and that should be considered in assessing the uncertainty associated with predictions. In this form errors in fitting observations are then treated as 'measurement error', even though the total model error derives from many different sources and is often larger than any conceivable real measurement error. An alternative approach is proposed, as a more rigorous implementation of the GLUE methodology. Arguments are developed to define an effective observation error, prior to the application of the model. The effective observation error may need to account for scale, heterogeneity, non-stationary error properties and other sources of incommensurability between model output variables and observables. Models that then fall outside of this allowable range are rejected. Models that fall inside the allowable range are used in prediction. The effects of input error, model structural error and effective observation error can, in principle, be separated. This modified GLUE approach is explored with examples using the rainfall-runoff model Dynamic TOPMODEL applied to discharge and fuzzy estimates of water table depths for 2 locations at Maimai catchment, New Zealand. The results have implications for how we, as modellers, consider observational uncertainties in the assessment of our model predictions.
H14A-08 17:45h
How good are hydraulic-conductivity data?
Mathematical theories gain utility in addressing ground-water problems by integration with site-specific data of all kinds. These data are always uncertain, and it is important to understand and quantify this uncertainty. Two studies conducted to evaluate hydraulic-conductivity data are reviewed and compared here. The first study involves a highly controlled intermediate-scale laboratory experiment constructed of clean sands with hydraulic conductivities that vary over about two orders of magnitude and are measured using permeameter and column experiments (Barth and others, 2001, WRR). The second study involves an extensively monitored field tracer test in fluvial deposits with hydraulic conductivities that vary over about 6 orders of magnitude and were measured using borehole flowmeters (Barlebo and others, 2004, WRR). In both studies, tracer tests were conducted and hydraulic heads measured. The hydraulic-conductivity measurements were evaluated by attempting to use them predictively in numerical flow and transport simulations of the systems. This resulted in predictions that matched the measured heads and concentrations more poorly than expected. The discrepancies are investigated by determining what hydraulic conductivities would be needed to reproduce the measured heads and concentrations, comparing these to the measured values, and considering whether the problem is the measured hydraulic conductivities or other aspects of the simulation. In the field problem, a system for evaluating the differences is proposed. Results suggest that this investigative approach can help understand errors in common types of data. Specifically, hydraulic-conductivity measurements are likely to be problematic enough that their use in ground-water model development needs to be considered carefully.
http://wwwbrr.cr.usgs.gov/projects/GW_ModUncert/