Simplification of one-dimensional hydraulic networks by automated processes evaluated on 1D/2D deterministic flood models

1D

One-dimension(al)

2D

Two-dimension(al)

CSI

Critical Success Index

DEM

Digital elevation model

EAD

Expected annual damage

GIS

Geographic information system

NC

No compensations – used when no compensations for volume and travel time have been included in the simplified model

SAHM

Simplification algorithm for 1D hydraulic network models

T###Mxxx

Notation of models only trimmed by ### mm

TxxxM###

Notation of models only merged by ### metres

T###M###

Notation of simplified models both trimmed by ### mm and merged by ### metres

Hydraulic models of urban drainage networks have been used for decades to evaluate the resilience of an area or test the effects of new infrastructure. With the main purpose of evaluating drainage capacities, for long it has been sufficient to simulate flows in the drainage network only. Naturally, these physically based deterministic models are now also commonly used to support decision-making for climate adaption structures and urban development plans (Field et al. 2012). However, climatic changes and urban development are causing an increase in size and frequency of urban flooding leading to a need for local measures to reduce the impacts (Field et al. 2012; IPCC 2014). This means that overland flows must be included in the hydraulic models (Henonin et al. 2013). Compared to one-dimensional (1D) surface models, a more realistic description of surface flow patterns is obtained by using coupled 1D/2D models (Leandro et al. 2009).

The coupling of a 1D network model and two-dimensional (2D) surface model (1D/2D) has significantly expanded the application areas of urban flood models and these models are now commonly used to predict the extents of urban flooding (Henonin et al. 2013; Russo et al. 2015). The shift from 1D/1D to 1D/2D models dramatically increases the computational demand (Leitão et al. 2010; Henonin et al. 2013; Van Dijk et al. 2014). The computational demand is of high importance for applications in flood warning systems or simulation of multiple scenarios (Leitão et al. 2010; Henonin et al. 2013; Meneses et al. 2015). Therefore, numerous attempts at speeding up 2D simulations are described in the literature including multi-layered coarse grid simulations (Chen et al. 2012), reduced complexity models (McMillan & Brasington 2007), and using a cellular automata approach (Ghimire et al. 2013).

The extensive work and knowledge gathered on computation of 2D models has shown promising results with reductions from days and hours down to minutes. With no change in the 1D network model, the computational demand of the 1D model thereby accounts for a larger share of the total computational demand of the 1D/2D model. Naturally, the next step is to reduce the computational demand of the 1D network models.

Numerous studies have been dedicated to improvement of 1D hydraulic network models using various approaches including conceptual models (Wolfs et al. 2013) or simply reducing the number of elements in the network (Leitão et al. 2010). However, few have looked into the effects on 2D surface model results when reducing the level of detail of the 1D network for a coupled 1D/2D model.

Simplification of hydraulic networks is often conducted manually or semi-automatically using a geographic information system. These procedures require numerous subjective decisions. Guidelines for network simplification are scarce and only a few unofficial documents on good practice exist, e.g., Wastewater Planning Users Group (2002). Errors due to wrongly or over-simplified models (models with structural deficits) have been widely neglected according to Del Giudice et al. (2015), who attempt to capture the combined errors of inputs and structural model errors in a stochastic term. However, structural model errors can be reduced by setting up procedures for how the model complexity can be lowered. Furthermore, an automated tool will enable a more consistent practice as well as reduce time and resources needed when implementing model simplification.

The purpose of this paper is to present an approach for automatic simplification of the 1D component in 1D/2D flood models. We apply two different methods for network simplification along with a combination making a third approach. The approaches include compensations for the simplifications. The performance of the simplified models is evaluated by comparing to a baseline consisting of the full 1D/2D model whereby further development of the approach is identified.

Three common approaches to network simplification are identified in Leitão et al. (2010), denoted pruning, trimming, and merging of links and nodes, respectively. Pruning is the most conservative method of only removing small, short links along main branches. This method has a very limited impact on computational demand and is rather a method to improve numeric model stability. Pruning is also included in the more comprehensive trimming approach that consists of deleting whole branches of links below a threshold for, e.g., diameter. Finally, merging involves joining multiple links to a single one by deleting nodes. Merging will maintain the extent of the network while trimming leads to the removal of the pipe network in some areas. Additionally, the approaches can be combined by merging links in an already trimmed model.

The trimming module in SAHM performs the exclusion of pipes and branches below a certain diameter threshold defined by the user. This approach requires information of the connected branches. To fulfil this, the trimming algorithm is recursive, thus a starting point is defined from where the algorithm moves through the network, as illustrated in Figure 1(b). For each node, SAHM will check upstream branches and whether all links within the branch are below the threshold diameter. If so, the branch is removed. Otherwise, the starting point moves one node upstream and the search is restarted from the new starting point. Figure 1(d) describes this procedure. In some cases, the branch contains a loop that may compromise the approach described to this point. To handle this, comparing nodes in the branch to previous start-nodes identifies a loop. A loop will only be removed when all links within the loop fulfil the conditions.

The merging module in SAHM joins two neighbouring links to one and removes the common node from the network. The condition for merging is a lower threshold on link length. Contrary to trimming, the merging approach only processes one link and its neighbouring links at a time, as illustrated in Figure 1(c). The approach for selection of links to merge is described in Figure 1(e). An extensive set of conditions needs to be fulfilled before two links are merged. Initially, the length of the link is compared to the minimum length threshold. If the link is within the threshold, checks with neighbouring links begin, otherwise the search continues to the next link. Links are unsuitable for merging if they are parallel, have different type of structure, or have large diameter differences. The user defines the diameter difference threshold. In addition, a node cannot be removed if it is an intersection between three or more links. When a link can be merged with links to both sides, the shortest one is selected for merging. Since the link resulting from merging two very short links can be shorter than the threshold, the merging of the network is repeated several times with gradually increasing lengths until the specified threshold is reached. As indicated in Figure 1(c), the total length of the pipe system is preserved, and hence the pipe length in the 1D simulation no longer corresponds to the physical length between the nodes in the reduced network.

Modifying the hydraulic network as described will change the characteristics of flow. We attempt to compensate for the changes by modifying the network volume and the travel times as described in the following.

Links with no or very low slope in the overall flow direction are assigned too long time delays when using this approach, since the acceleration, pressure and momentum descriptions from the Saint-Venant equations are neglected in the Manning equation used for the velocity approximation. Therefore, a threshold for minimum velocity is introduced for u in Equation (1). The threshold of minimum velocity has been defined to 0.15 m/s based on Wallington charts (Butler & Davis 2011). If the computed velocity for a link is below this threshold, the velocity of the upstream neighbouring link is applied if this exceeds the threshold. Otherwise, the threshold value is assumed as the velocity for the link in the estimation of time compensation.

The simplified models are compared to the baseline model by means of traditional metrics such as computation time, hydrographs and mass balances. We also introduce two metrics that assess the importance of the spatial distribution of the model errors in their typical use, i.e., calculation of hazard maps and overall risk of flooding in the catchment. The metrics are described below.

Flood risk is often summarised as the expected annual damage (EAD) (Zhou et al. 2012). The EAD is computed from the damage costs and hence differences in EAD will indicate the ability of the simplified models to generate results that are correct on the catchment level in relation to decision-making.

The fully dynamic Saint-Venant equations are used for calculating flow in the 1D network via the six-point Abbott-scheme. Flow in the 2D model is simulated using the full shallow water equations with a higher order numerical scheme and a finite volume method. For additional information on the 2D solution scheme used in MIKE FLOOD, see DHI (2014, 2015). The two models are linked at each node using a virtual orifice for calculation of water exchange.

The hydraulic network primarily consists of circular links draining most catchments. A large open channel drains the area from mid-west to the northwest as the main outlet to the sea. Two additional outlets are located north and south of the main outlet. Both of these are closed rectangular channels with the southern one connected to the open channel, while the other drains the northern part of the network. The northwest part of the catchment is a low-lying area exposed to flooding from high sea levels. In this study, the sea level is kept constant at an elevation of 0 metres as we focus on flooding from the drainage system only. The upstream part of the catchment is steeper and flooding in this area is caused by precipitation only.

A baseline is produced from model simulations with different rain inputs. Design rain inputs with return periods of 2, 5, 10, 20 and 100 years were obtained from the Australian Bureau of Meteorology (BOM 2016) and are used for simulation. To obtain an indication of the uncertainty of the simulated flood extent resulting from other sources than simplification we have increased and decreased the rain volume by 23%, corresponding to the overall uncertainty of runoff according to Hansen & Liu (2004).

The simulations were conducted using the MIKE FLOOD Message Passing Interface (MPI) limited to 7 threads on a HP EliteDesk 800 G2 TWR with Intel i7-6700 3.40 GHz CPU and 16 GB RAM.

Hydrographs from the 1D hydraulic network model are inspected to locate potential changes in flow characteristics after simplifying the network.

The hydrographs for an upstream link (Figure 5(d)) suggest that the simplified models slightly overestimate peak flows while the timing of peaks varies slightly. The TxxxM100 model is delayed by a minute while the T500Mxxx and T500M100 models peak a few minutes early. The time variations are smaller than in the models without compensations (not shown), thus the time compensation works as intended with improved fit of the initial peak to the baseline even at places where trimming has removed a large part of the network. The Manning equation, used for calculation of the time compensations, describes flow processes in a more simplified manner than the Saint-Venant equations, leading to the small variations in peak time. After 2–4 hours of the simulation period, the flow is in many cases not as accurate with the decline starting earlier or later than the baseline. This may also be caused by changes in the surface flooding when storage and flow-paths change from the baseline.

Except for overestimation of the volumes of the merged models for low return periods, there are no general tendencies to observe with respect to the amount of simplification. For some return periods, higher degrees of model simplification lead to smaller changes than lower degrees of model simplification and vice versa.

The impacts of simplification in the 1D network model on the 2D surface results are presented in the following section.

The difference in spatial distribution of flooding is illustrated in Figure 8 as spatial hits, misses and false positives for the most simplified models, along with the maximum water depth of the baseline during a 100-year event. As shown in Figure 8(b)–8(d), the trimming approach may cause deletion of connections in locations where the full 1D model surcharges, whereby the water will surcharge at the nearby branches in the reduced model. The merging approach also leads to changes in the spatial distribution of flooding but to a much lesser extent than trimming.

This indicates that flooding may have moved from one location to another. This is also visible in Figure 8 where flooding in trimmed models occurs downstream in the larger branches instead of the outer branches. Inspection of the simulations shows that the spatial changes are, in many cases, limited to distances of a few pixels, hence these errors may be of little importance for many applications. This is tested by calculating the costs of flooding for a range of return periods and by calculating the EAD using the approach presented by Olsen et al. (2015).

The influence of the implemented compensations is investigated for all three approaches to validate if the compensations improve the results.

Including compensations for volume loss kept the total network volume deficit within 0.2% compared to 6% in the non-compensated T500M100 model.

In the 1D hydrographs, the peak arrival time and peak flow obtains a better fit to the baseline in the compensated models. In non-compensated models, the initial peak arrives earlier than in the baseline and compensated models, hence the approach for time-compensation is working as anticipated.

Despite a network volume deficit of 4.3% and 5.5% for the non-compensated T500Mxxx and T500M100 models, respectively, the 1D/2D water exchange values are better when neglecting the volume compensations. Additionally, the non-compensated TxxxM100 model yields similar or improved hydrographs as compared to the compensated model. Thus, it is likely that the manhole size has a more significant effect on the 1D/2D interactions than the network volume deficit and it may be beneficial to use a different approach for implementation of volume compensations, or to simply avoid the compensation scheme.

The spatial errors of the non-compensated models are shown as black symbols in Figure 9, and indicate that compensations for volume losses and travel time are of little importance for the spatial flood distribution. In Figure 11, compensations slightly improve EAD in the TxxxM100 and T500M100 models while EAD for T500Mxxx is worse than the T500Mxxx-NC model.

Overall, the compensations improve the results of the 1D hydrographs and flood area. However, compensations have only slightly positive or a negative effect on results of water exchange, CSI, total damage cost and EAD. Only when applying the compensations, outflow from the 1D network to the 2D surface varies significantly from the baseline. However, the inflow from the 2D surface to 1D network increase or decrease correspondingly with the changes in outflow, resulting in a net decrease in flooded surface area.

When accurate hydrographs are of high priority, compensation for travel time may be justified. The small changes in travel time however have little effect on 2D results. Compensating for volume loss by changing manhole diameters is also not recommended as this leads to decreasing accuracy of the 2D model results.

It was possible to reduce the computation time of 1D/2D simulations by 35%, exclusively by modifying the 1D hydraulic network model. The overall resulting calculated EAD changed remarkably little even when applying quite aggressive model simplifications. However, other metrics varied systematically as a function of the model simplification. Hence, the type and degree of model simplification that can be justified seems to depend on what the model is used for.

Even though the calculated hydrographs overall showed good agreement for different levels of simplification, the simplifications proved to have an impact on the 1D hydraulic network. The main change was identified as an overestimation of flow along main branches, occurring mostly when applying merging. The effect may be reduced by increasing energy losses, e.g., by decreasing Manning numbers, where features have been deleted.

The simplification of the 1D network model also influenced the exchange between the 1D and the 2D parts of the model, mainly for trimmed models. In general, this led to fewer locations with floods but larger flooding at these locations. This cancellation of errors is the main reason why the overall EAD seems to be rather accurate in spite of a high degree of model simplification. However, for moderate return periods there will be rather large and systematic differences in the spatial distribution of flooding in the catchment. Since flooding during events with small return periods constitutes a large part of the overall risk, the degree of simplification of the 1D network is important in identifying potential measures to reduce the risk. Hence, the impact of 1D model simplification seems to have the potential of reducing calculation times considerably, but at the expense of less knowledge of where in the catchment the flooding occurs for smaller return periods.

Studies could be undertaken to see whether including features of the 2D model in the simplification in the 1D model would lead to better results. The starting point could be to put constraints on simplifications close to and in local depressions. For merging, it could be hypothesised that the key would be to include nodes in the depressions, whereas for trimming it might be important to retain links to areas with depressions.

In this study, a simplification algorithm for 1D hydraulic network models (SAHM) is developed as an automatic simplification approach. The resources spend on model simplifications are substantially reduced compared to manual or semi-automatic procedures. Additionally, the procedures are streamlined between users, with a common set of checks conducted prior to removal of a link or node. A guideline of inputs to SAHM, e.g., thresholds depending on the modelling purpose, may be an advantage to avoid over- or under-simplified models. This may be an advantage even when employing only 1D models. However, in our case, the main focus is on how such simplifications impact simulations of pluvial flooding.

The simplification of a network with more than 20,000 elements is conducted within a few minutes using merging, trimming or a combined simplification method. Using the developed approach, the computation time for the 1D/2D simulation decreases by 35% after removing 66% of the elements in the 1D hydraulic network model. The simplified models are compensated for volume losses and travel time differences. The approach of implementing compensations for travel time leads to small improvements in 1D hydrographs of the hydraulic network model while compensating for volume losses of deleted features leads to a decline in accuracy of CSI and EAD.

1D hydrographs of the hydraulic network model show little variation between the baseline and simplified models but overestimation of flow in main branches. Spatial deviations of the 2D flood models are evaluated using the CSI and indicate that these models are highly influenced by the level of detail of the 1D hydraulic network. Thus, it is necessary to exercise caution when using simplified 1D/2D urban flood models for flood hazard assessments and design purposes. Calculation of the EAD is considerably less sensitive to model simplifications, with merging considerably more accurate than trimming. Suggestions for how the procedure can be improved further are given. For instance, maintaining connection to depressions may be a main objective to improve the accuracy of the reduced model. Overall, it already seems feasible to be able to derive simpler flood models without compromising the accuracy in an unacceptable manner.

This research has been financially supported by the Australian Government through the CRC for Water Sensitive Cities. The catchment data were kindly provided by Melbourne Water and the City of Port Philip. We thank Christian Urich (Monash University), Mohanasundar Radhakrishnan (UNESCO-IHE) and Jens Toke (DTU) for their support in setting up the hydraulic model for the catchment.