Distributed physically based models may be subject to additional uncertainty because the partial differential equation systems of these models often cannot be solved analytically (unless very simple boundary conditions are assumed). They rely on approximate numerical solutions and therefore, numerical diffusion and other inaccuracies may occur, depending on the numerical implementation used. For example, Bates at al. (1997) investigated different numerical techniques for flood inundation models and show a clear impact on model predictions. Other studies find only a minor impact due to numerical solution (Bates et al., 1995; van Looveren et al., 2000). This indicates a complex interaction between numerical solutions and other model parameters as well as boundary conditions. For example, many cell based flood inundation models use a flow limiter, which restricts the amount of water that can flow from one cell to another within a time-step, to damp numerical oscillation and allow the model to remain stable. However, this flow limiter directly affects the uncertainty and sensitivity of the floodplain surface roughness (in this particular case it made the parameter insensitive). In fact, the number of parameters which have to be chosen for a numerical scheme can be so large that they have to be investigated in a ‘stand-alone’ uncertainty or Sensitivity Analysis (see e.g. Claxton, 2002). Similar numerical approximations can also arise in other types of models, such the predictions obtained may not be an accurate solution of the original conceptual model equations (e.g. Kavetski et al., 2003), depending on the scale and resolution of the numerical approximations. The choice of scale and resolution may also be expected to interact with the effective values of the parameters and boundary conditions required by the model.

Thus, in general, the procedural models that provide quantitative predictions will only be an approximation of the real processes (and, in some cases, of the equations of the conceptual model). There will therefore always be some uncertainty associated with the choice of a particular model structure and implementation. Given the other sources of uncertainty in the modelling process, however, it has proven very difficult to separate out the model structural and implementation uncertainty]or even to give guidance about what procedural model (model structure and implementation method) to use in different circumstances. The use of model calibration or conditioning on observations allows (to some extent) the effects of model structural and implementation error and input error to be compensated by change in effective parameter values.

References

Bates, P.D., Anderson, M.G. and Hervouet, J.M., 1995. Initial Comparison of 2 2-Dimensional Finite-Element Codes for River Flood Simulation. Proceedings of the Institution of Civil Engineers-Water Maritime and Energy, 112(3): 238-248.

Bates, P.D., Anderson, M.G., Hervouet, J.M. and Hawkes, J.C., 1997. Investigating the behaviour of two-dimensional finite element models of compound channel flow. Earth Surface Processes and Landforms, 22(1): 3-17.

Claxton, A., 2002. Modelling subsurface water and chemical transport through floodplain systems, Bristol University, Bristol.

Kavetski, D., Kuczera, G. and Franks, S.W., 2003. Semidistributed hydrological modeling: A "saturation path" perspective on TOPMODEL and VIC. Water Resources Research, 39(9): art. no.-1246.

van Looveren, R., Willems, P., Sas, M., Bogliotti, C. and Berlamont, J., 2000. Comparison of the software packages ISIS and Mike 11 for the simulation of open channel flow. In: W.R. Blain and C.A. Brebrian (Editors), Hydraulic Engineering Software. WITPress?, Southampton, pp. 3-14.

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Risk and Uncertainty (Description and Definition)