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The choices made in effecting the procedural model will normally involve the choice of scale and resolution at which the calculations will be made. For the nonlinear equations common in environmental modelling problems, the sensitivity of solutions to space and time resolution can generally only be estimated locally, but it can be expected that there will be an interaction between scale and resolution and the effective values of the parameters required by a model. The effects of spatial resolution on models have been explored by various authors (Bashford et al., 2002; Blöschl et al., 1997; Horritt and Bates, 2001). For example Hardy et al. (1999) and Yu and Lane (in press-a) found that spatial resolution has a major effect on inundation extent and flow predictions. Different processes will be dominant on different [[Scale]]s and it can be argued that, in the nonlinear case, a model which is applicable at a small scale may require a different formulation to be used on a larger scale (Beven, 1995; Yu and Lane, in press-b). In particular, the effects of sub-grid heterogeneity are expected to be more important with increasing scale and mesh size (Beven, 1995). Thus, the values of model parameters required in a model formulation might also change with changing scale or resolution. This creates difficulties in estimating parameters that it is actually possible to measure in the field. For example, a roughness coefficient for flow over a flood plain or in a river channel, might be inferred from velocity profiles at a point on the flood plain or a cross-section of a channel. This will not, however, be the value required in a discretised model of the flow domain that will need to reflect changing geometry and surface characteristics (e.g. pool-riffle structures in a channel, effects of vegetation, hedges and walls on the flood plain). Similar arguments can be made about many other “measureable” parameters. For example the hydraulic conductivity, which can be determined by measurements at the point scale (Mualem, 1986), but is often difficult to reconcile on a grid cell (Beven, 1989). The parameter values required by the model will be ‘effective’ rather than ‘real’ and the values required by the model might be incommensurate with values that are measured at a different scale in the field. Many other model parameters are ill-defined or have no basis for estimation at all. Even where parameter measurements can be made, there will also always be uncertainty in extrapolating from points where there are measurements to other points in the flow domain. Thus, it may never be possible to determine such a parameter everywhere in a distributed model without uncertainty, considering not only the scaling issue above, but also the uniqueness of place argument by Beven (2000). Even when a perfect model structure is assumed, it will be difficult to determine the parameters from one place to another, because of the specific characteristics of each site and the problems in scaling. Recent progress in remote sensing increases the possibilities to determine spatial patterns of parameters. In this way it might be possible to estimate parameters such as the Manning surface roughness and apply them within flood inundation models (Bates et al., 1997; Wilson, 2004), though, the effective values of parameters required by a model may still be dependent on model implementation and boundary conditions. Some uncertainty in estimating effective values will therefore necessarily remain. Remote sensing offers considerable opportunities to acquire information about a large number of distributed input parameters (Schultz, 1996), although it should not be forgotten that additional models (with additional parameters) have to be applied to process the remotely sensed information. Such a sub-model will also be liable to uncertainty (see e.g. Eineder, 2003). == References == Bashford, K.E., Beven, K.J. and Young, P.C., 2002. Observational data and scale-dependent parameterizations: explorations using a virtual hydrological reality. Hydrological Processes, 16(2): 293-312. Bates, P.D., Horritt, M.S., Smith, C.N. and Mason, D., 1997. Integrating remote sensing observations of flood hydrology and hydraulic modelling. Hydrological Processes, 11(14): 1777-1795. Beven, K.J., 1989. Changing Ideas in Hydrology: The Case of Physically Based Models. Journal of Hydrology, 105: 157-172. Beven, K.J., 1995. Linking Parameters across Scales - Subgrid Parameterizations and [Scale]-Dependent Hydrological Models. Hydrological Processes, 9(5-6): 507-525. Beven, K.J., 2000. Uniqueness of place and process representations in hydrological modelling. Hydrology and Earth System Sciences, 4(2): 203. Blöschl, G., Sivapalan, M., Gupta, V., Beven, K.J. and Lettenmaier, D., 1997. Preface to the special section on scale problems in hydrology. Water Resources Research, 33(12): 2881-2881. Eineder, M., 2003. Efficient simulation of SAR interferograms of large areas and of rugged terrain. IEEE Transactions on Geoscience and Remote Sensing, 41(6): 1415-1427. Hardy, R.J., Bates, P.D. and Anderson, M.G., 1999. The importance of spatial resolution in hydraulic models for floodplain environments. Journal of Hydrology, 216(1-2): 124-136. Horritt, M.S. and Bates, P.D., 2001. Effects of spatial resolution on a raster based model of flood flow. Journal of Hydrology, 253(1-4): 239-249. Mualem, Y., 1986. Hydraulic conductivity of unsaturated soils: predictions and formulas. In: A. Klute (Editor), Methods of soil analysis. Part1. Agronomy Society of America, Madison, pp. 799-823. Schultz, G.A., 1996. Remote sensing applications to hydrology: Runoff. Hydrological Sciences Journal-Journal Des Sciences Hydrologiques, 41(4): 453-475. Wilson, M.D., 2004. Evaluating the effect of data and data uncertainty on predictions of flood inundation, University of Southampton, Southampton, 276 pp. Yu, D. and Lane, S.N., in press-a. Urban fluvial flood modelling using a two-dimensional diffusion wave treatment: 1. Mesh resolution effects. Yu, D. and Lane, S.N., in press-b. Urban fluvial flood modelling using a two-dimensional diffusion wave treatment: 2. Development of a sub grid-scale treatment. == Go to == [Risk and Uncertainty (Description and Definition)]
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