Topography and computational grid resolution

The inundation model used for the work in this chapter used the same Clawpack code as in chapters 4 and 5. The terrain elevation data for the simulations was adapted from the 75m resolution elevation data used in Garcia-Pintado et al. [2015] and Garcia-Pintado et al. [2013]; this was based on upscaling the NEXTMAP British digital terrain model (Intermap Technologies).

Figure 6.1 shows the terrain elevation in m used for our inundation simulations, with three gauge locations. Data from gauges at Knightsford Bridge and Worcester Barbourne were used to drive the model inflows; data from the gauge at Saxon’s Lode were used for validation of results. Gauge data were not assimilated. The domain includes a stretch of the river Severn (traversing north-south) north of Tewkesbury, U.K. The domain also includes part of the river Teme (east-west), which is one of the Severn’s larger tributaries. We used reflecting boundaries at the north, east and west boundaries of the domain, and an extrapolating outflow boundary at the southern end of the domain in order to allow water to flow out freely.

It was necessary to make changes to the elevation used in Garcia-Pintado et al. [2015] and Garcia-Pintado et al. [2013] due to differences in the way Clawpack and Lisflood-FP represent topography. Lisflood-FP uses a sophisticated sub grid parameterisation tech- nique to represent river channels (see Neal et al. [2012a]). This gives the model the capa- bility to use low resolution digital terrain maps while still resolving all the river channels; the 30-50m wide rivers in the Severn-Avon catchment can therefore be accurately repre- sented using a 75m grid resolution. This sub-grid approach was used in Garcia-Pintado et al. [2015] and Garcia-Pintado et al. [2013] to model river channels in LISFLOOD-FP as rectangular cross sections, with paramaterised depths and widths of the channels chosen to match measured cross sections. Clawpack does not have sub-grid capability. Since we used the 75m terrain model, we necessarily assumed the river channels were all 75m wide and adapted the bed elevation in the river model cells in order to satisfy the requirements that:

Chapter 6: New observation operator for inundation forecasting - case study.

Figure 6.1: Experimental domain, elevation shown in metres. Axes co-ordinates (x and y) are OSGB 1936 British National Grid projection in m. White circles show the location of gauges. Data from Knightsford Bridge and Worcester are used for inflow generation. Data from the Saxon’s Lode gauge are used for comparison with model prediction.

• the cross sectional area of the channels approximates the parameterised cross sec- tional area used in Garcia-Pintado et al. [2015] and Garcia-Pintado et al. [2013] and

• the bed elevations are smoothly varying.

We found that matching the cross sectional area exactly in each river grid cell meant that the bed elevations were not smooth enough to accurately represent the rivers. Some river cells had bed elevations much higher than all their neighbours, resulting in water going out of bank in unrealistic conditions (i.e. even for very low flows, and in areas that do not show flooding on the SAR images). We therefore smoothed the bed eleva- tions to generate more realistic behaviour. All models of this type are required to make approximations and parameterisations for river and floodplain topography, resulting in

flows which are not completely realistic. Nevertheless, the updates generated using our new observation operator are still of interest as we are able to examine the impact of the observations and assess to what extent the data assimilation is able to compensate for the inaccuracies of the model.

Although Clawpack does not have sub-grid capabilities, it is possible to specify a computational grid resolution that is different to the topography resolution. We therefore used a computational grid resolution of 25m with the topography grid of 75m resolution. This means that each topography grid cell was split into nine smaller cells for calculation of the solution, each with the same elevation defined by the topography map. Each 75m-wide river cross section is therefore modelled by three 25m grid cells. Using this finer resolution for the computational grid results in longer run times for the simulation experiments, but we found it was necessary in order that the simulated flow rates matched the measured flow rates at the Saxon’s Lode gauging station at low flows. To illustrate this, we used reported flow rates from Knightsford Bridge and Worcester Barbourne over a (no flooding, low-flow) 10 day period before the floods as driving inflow and measured the resulting model prediction at the location of the Saxon’s Lode gauge. The simulation period here runs from 0100 11th November 2012 to 0100 21st November 2012.

Figure 6.2: Measured and modelled flow rates at Saxon’s Lode gauge location. The

red crosses show measured hourly values. The blue line is modelled flow rate for 75m computational grid resolution, the green line is modelled flow rate for 25m computational grid resolution; all other experimental conditions and model parameters are the same.

Figure 6.2 shows modelled flow rates at the location of the Saxon’s Lode gauging station for 25m (green line) and 75m (blue line) resolution computational grid. In both cases the Manning’s friction coefficients were set to 0.02 in the river channels and 0.06 elsewhere. The red crosses show hourly flow rates reported by the Environment Agency

Chapter 6: New observation operator for inundation forecasting - case study.

at the gauge. The discharge spikes seen in the observed data are due to tidal backwater effects, sometimes observed at this location (Neal [personal communication, 2019]). This figure shows that our model is unable to successfully reproduce the in-bank flow rates when using the 75m resolution computational grid; this was true for a range of realistic channel friction parameter values. Using a 25m resolution grid gives results that match the reported values better. The increased computational cost of running the model at 25m resolution is the main reason for using a subdomain of the area covered by the SAR observations.

It was also necessary to switch off terrain interpolation in Clawpack for the elevation model. Clawpack is designed to take a (coarse) topography map and interpolate model cell corner elevations in order to give a good approximation for the elevations of the terrain in the centre of each computational cell. In the case of a river profile, this can have the effect of changing the cross section of the river channel. In order to use the bed elevations that were specified with no additional smoothing it was necessary to write a new ‘no-interpolation method’ to set up the topography exactly as specified.