Targets-specified grids-tailored sub-model approach for fast large-scale high-resolution 2 D 1 urban flood modelling 2

Abstract. The accuracy of two-dimensional urban flood models (2D models) is improved when high-resolution Digital Elevation Models (DEMs) is used, but the entailed high spatial discretisation results in excessive computational expenses, thus prohibiting the use of 2D models in real-time forecasting at a large scale. This paper presents a sub-model approach to tailoring high-resolution 2D model grids according to specified targets, and thus such tailor-made sub-model yields fast processing without significant loss of accuracy. Among the numerous sinks detected from full-basin high-resolution DEMs, the computationally important ones are determined using a proposed Volume Ratio Sink Screening method. Also, the drainage basin is discretised into a collection of sub-impact zones according to those sinks' spatial configuration. When adding full-basin distributed static rainfall, the drainage basin's flow conditions are modelled as a 1D static flow by using a fast-inundation spreading algorithm. Next, sub-impact zones relevant to the targets' local inundation process can be identified by tracing the 1D flow continuity, and thus suggest the critical computational cells from the high-resolution model grids on the basis of the spatial intersection. In MIKE FLOOD's 2D simulations, those screened cells configure the reduced computational domains as well as the optimised boundary conditions, which ultimately enables the fast 2D prediction in the tailor-made sub-model. To validate the method, model experiments were designed to test the impact of the reduced computational domains and the optimised boundary conditions separately. Further, the general applicability and the robustness of the sub-model approach were evaluated by targeting at four focus areas representing different catchment terrain morphologies as well as different rainfall return periods of 1–100 years. The sub-model approach resulted in a 45–553 times faster processing with a 99 % reduction in the number of computational cells for all four cases; the predicted flood extents, depths and flow velocities showed only marginal discrepancies with Root Mean Square Errors (RMSE) below 1.5 cm. As such, this approach reduces the 2D models' computing expenses significantly, thus paving the way for large-scale high-resolution 2D real-time forecasting.


. In order to mitigate the flood risks and the related consequences, a flood 36 forecasting system that complies with two criteria: i) accurate spatial and temporal flood predictions and ii) 37 sufficient lead time between rainfall predictions and flood predictions, is considered as a prerequisite to provide 38 precise early warnings for decision makers. Therefore, with the purpose of identifying an accurate and timely 39 urban flood model to configure such a system, we review two types of models: i) 2D hydrodynamic models 40 (Section 1.1) and ii) 1D static models (Section 1.2). After summarising the strengths and potentials for the two 41 models, the scientific innovation of the proposed approach is outlined by identifying a 1D/2D complementary  (Bernini and Franchini, 2013), also known as the "flat water assumption" 91 (Zerger et al., 2002) is commonly embedded as the underlying algorithm in these models. With mass 92 conservation as the only governing law and disregarding temporal evolution, the fast-inundation spreading 93 models present a filling/spilling process within the predefined flow patterns thus resulting in predictions 94 rapidly. Here, we name the process "1D static flow" in this research. These models are divided into two types 95 (

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In general, sinks are classified into two categories: actual sinks and artefacts (Lindsay and Creed, 2006). To 150 preserve the actual sinks only, the DEM's vertical accuracy is used, whereby artefact sinks shallower than or 151 equal to this threshold value are removed. Other sink artefacts, such as detected inside enclosed building blocks 152 or on rooftops, are deleted (see Fig. 3a). Nevertheless, the inclusion of all actual sinks as computational nodes 153 may lead to massive computational costs while improving minor modelling accuracy for network-based 154 computations (i.e. 1D static/dynamic modelling). To further differentiate "important" from "unimportant" 155 sinks in light of the computational efficiency, the Hydrological Retention Volume Ratio ( ratio HRV ) is defined 156 as the ratio between a sink's capacity (volume) and the runoff volume generated from its associated 157 contributing catchment, which reflects the sink's runoff retention performance (strong/poor) relative to rainfall 158 amounts, see Eq. (1) and (2). So, if we consider the spill-over as a transition moment when a sink uses up all 159 retention capacities and generates runoff only, then "unimportant" sinks that make quicker spill-over during a 160 rain event should be modelled as part of catchments rather than having retention capacities. To substitute those 161 catchments from screened "unimportant" sinks, "important" sinks should initiate another round of catchment 162 delineation (drainage basin discretisation) resulting in "dissolved catchments", see  where Csink is the sink's capacity; Rcellsize is the cell size of the 2D rainfall (distributed dynamic rainfall) that has 166 the commensurate cell size of DEMs; Ai is the total rainfall contained by cell i in the total rainfall raster 167 (distributed static rainfall) that is aggregated from the 2D rainfall, and n is the total number of rainfall cells 168 within each sink's catchment. S1 and S2 are the accumulated rainfall from the hyetograph before and after the 169 unimportant sinks start spilling over. This means that an equivalent proportion is shared between this volume 170 ratio and the percentile of the rainfall hyetograph. Therefore, to determine such a parameter, the accumulated 171 rainfall amount that indicates a spilling moment for the unimportant sinks can act as a reference.

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Since volume losses associated with removed "unimportant" sinks may accumulate to significant volume due 173 to stream branch convergences, the Volume Loss Ratio (VLratio), see Eq.
(3), is introduced. This ratio is defined 174 as the aggregated volume loss in removed sinks vs. the downstream "important" sinks' retention capacities.

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The aggregated volume loss is calculated as shown in Eq. (4) and depends on the volume and number of 176  where VLAggr. is the aggregated volume losses; Vi is the volume loss from the identified "unimportant" sink i, 183 and n is the number of sinks located within the dissolved catchment (see Fig. 3b).  , . - where Vspilled represents excess volumes once the spill-over level is reached and Vremaining is the actual volume 246 retained locally, and Vreceived represents the converged flow volumes received from upstream connecting links.

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Csink, Aggr. is obtained from Section 2.1. After enabling this algorithm, a stream link feature class incorporating geometric features and their associated attribute table is produced ( Fig. 5a

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An extreme precipitation event on July 2 nd , 2011 was selected. Due to the large extent of the Greve basin, we 417 used data from five available rain gauges to cover the basin-wise rainfall heterogeneities (see Fig. 9). The

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Thiessen polygon approach was applied to distribute precipitation data from these rain gauges onto their 419 nearest neighbourhoods (Fig. 9), simulating the pattern of the progressively decreasing rainfall from the eastern 420 coastline towards western inland. According to the time-series of I5805 (shown as hyetographs in Fig. 9), the 421 overall simulation time of 172 minutes was used for MIKE FLOOD, where the simulation continued for 97 422 minutes after the main peak, allowing for the sufficient time for flood peaks to flow through the landscape. The HRVratio parameter was set to 15%, considering that the corresponding accumulated rainfall (i.e. 14.8 mm 428 = 15% × 98.6 mm, gauge I5805) is relatively small compared to the total. Next, a VLratio of 5% was applied to    the discrepancies of maximum depth flood extents, binary analyses (dry/wet) from the status of the flooded 451 cells were conducted ( Fig. 11a and b)

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Apparently, for these positions, the sub-model approach produced significantly fewer over-predictions for the 485 downstream boundary than did the municipality domain approach.

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The histograms of maximum depth differences are displayed in Fig. 11e and f  To clarify discrepancies in spatial-temporal flow developments, hydrographs including water depths and flow 501 velocity in u-and v-directions were extracted for the three approaches ( Fig. 12a and b). Two runoff patterns 502 each containing 6 points were selected as a simplified representation of runoff dynamics in the focus area A 503 (see Fig. 8

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As opposed to the full-domain approach that implies general modelling targets, the sub-model 698 approach provides no flood information outside the focus areas. However, the independency in-699 between various sub-models is a substantial advantage to parallel process many small sub-models in