Quantifying the importance of spatial resolution and other factors through global sensitivity analysis of a flood inundation model. Water Resources

Where high resolution topographic data are available, modellers are faced with the decision 19 of whether it is better to spend computational resource on resolving topography at finer 20 resolutions or on running more simulations to account for various uncertain input factors (e.g. 21 model parameters). In this paper we apply Global Sensitivity Analysis to explore how 22 influential the choice of spatial resolution is when compared to uncertainties in the 23 Manning’s friction coefficient parameters, the inflow hydrograph, and those stemming from 24 the coarsening of topographic data used to produce Digital Elevation Models (DEMs).. We 25 apply the hydraulic model LISFLOOD-FP to produce several temporally and spatially 26 variable model outputs that represent different aspects of flood inundation processes, 27 including flood extent, water depth and time of inundation. We find that the most influential 28 input factor for flood extent predictions changes during the flood event, starting with the 29 inflow hydrograph during the rising limb before switching to the channel friction parameter 30 during peak flood inundation, and finally to the floodplain friction parameter during the 31 drying phase of the flood event. Spatial resolution and uncertainty introduced by resampling 32 topographic data to coarser resolutions are much more important for water depth predictions, 33 which are also sensitive to different input factors spatially and temporally. Our findings 34 indicate that the sensitivity of LISFLOOD-FP predictions is more complex than previously 35 thought. Consequently, the input factors that modellers should prioritise will differ depending 36 on the model output assessed, and the location and time of when and where this output is 37 most relevant.

influential the choice of spatial resolution is when compared to uncertainties in the 23 Manning's friction coefficient parameters, the inflow hydrograph, and those stemming from 24 the coarsening of topographic data used to produce Digital Elevation Models (DEMs).. We 25 apply the hydraulic model LISFLOOD-FP to produce several temporally and spatially 26 variable model outputs that represent different aspects of flood inundation processes, 27 including flood extent, water depth and time of inundation. We find that the most influential 28 input factor for flood extent predictions changes during the flood event, starting with the 29 inflow hydrograph during the rising limb before switching to the channel friction parameter  (Bradbrook et al., 2004), whilst models run in an unsteady state enable modellers to 55 understand the dynamic variation of flood hazard throughout the passage of the flood wave 56 (e.g. Bates and De Roo, 2000;Mignot et al., 2006;Skinner et al., 2015). The application of 57 these models has allowed the mapping of regions at risk of inundation from coastal (e.g. topographic data is commonly resampled to a coarser resolution than its original form, 99 however the choice of method applied to produce the coarser DEM can result in different 100 model predictions (Fewtrell et al., 2008).

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The development of more spatially complex models opens up a complexity-uncertainty trade 103 off, whereby for a given amount of computational resource the total number of Monte Carlo 104 simulations that can be run to quantify uncertainty in model predictions is limited by the 105 spatial complexity of the model. One example of this issue is described by Beven et al. (2015) 106 where the requirement for multiple simulations for forecast ensembles competes with the 107 increasing spatial complexity of models. Despite the increasing availability of high quality 108 data, the continued improvement in hydraulic models and computational advances, one of the 109 key barriers for a more widespread uptake of flood inundation models for decision making 110 during emergency situations is the time taken to perform simulations (Leskens et al., 2014).

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The case study area used in this application is the Imera basin in Sicily which covers an area

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The key idea of variance-based Sensitivity Analysis is to measure the relative influence of the 231 uncertainty in each input factor by its contribution to the variance of the model output. In   Conversely, models can also be run at finer resolutions, however given that the floodplain is 326 predominantly rural, we felt that it was not necessary to resolve length scales finer than 10 m.   The bottom panel of Figure 3 reports the difference between the total-order sensitivity index  we see is that the hydrograph appears to be most influential factor at a location first, followed

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The bottom panel of Figure 4 indicates that there are also spatial variations of the sensitivity 565 of the initial and maximum inundation timings. As with water depth, there is significant 566 spatial variability in determining the most influential input factor. The factor most influential 567 for the time of initial inundation is not necessarily the same as the factor most influential for perturbations the maximum discharge is reached one hour earlier than for others (Figure 1).

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Any location that is influenced by spatial resolution or the DEM for one output is likely to be 576 influenced by the same factor for the other output. This indicates that the pattern of surface 577 elevation is having a significant effect on the routing of flood waters to these locations.

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That is, none of the input factors have been classified as influential (or not) due to 605 unreasonably large (or small) bounds in the sampling range. In other cases where the number 606 of parameters is much larger it may be that a subset of influential factors is identified more 607 easily (e.g. Dobler and Pappenberger, 2013). 608 We have shown that using lumped outputs alone may hide temporal and spatial variability in

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This study has applied a GSA methodology, which allowed us to assess whether variability in representation, boundary condition data, parameter classification or model structures.

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Finally, the approach adopted in this paper to include discrete, non-numerical choices within 728 a GSA and to explore how sensitivity changes in time and space could be adopted by any