Integration of hillslope hydrology and 2D hydraulic modelling for natural ﬂ ood management

Natural ﬂ ood management (NFM) has recently invigorated the hydrological community into redeploying its process understanding of hydrology and hydraulics to try to quantify the impacts of many distributed, ‘ nature-based ’ measures on the whole-catchment response. Advances in spatial data analysis, distributed hydrological modelling and fast numerical ﬂ ow equation solvers mean that whole-catchment modelling including computationally intensive uncertainty analyses are now possible, although perhaps the community has not yet converged on the best overall parsimonious framework. To model the effects of tree-planting, we need to understand changes to wet canopy evaporation, surface roughness and in ﬁ ltration rates; to model inline storage created by ‘ leaky barriers ’ or of ﬂ ine storage, we need accurate channel hydraulics to understand the changes to attenuation; to model the complex behaviour of the whole network of NFM measures, and the possibility of ﬂ ood peak synchronisation effects, we need ef ﬁ cient realistic routing models, linked to key ﬂ ow pathways that take into account the main physical processes in soils and the antecedent moisture conditions for a range of different rainfall events. This paper presents a new framework to achieve this, based on a cascade of the Dynamic Topmodel runoff generation model and the JFlow or HEC-RAS 2D hydraulic models, with an application to the Swindale Catchment in Cumbria, UK. We demonstrate the approach to quantify both the effectiveness of a relatively large ‘ runoff attenuation feature ’ in the landscape and the uncertainty in the calculation given model parameter uncertainty.


INTRODUCTION
There has been a growing number of investigations attempt- and river restoration including re-meandering and floodplain reconnection to hold back and temporarily store more water which has been popular across Europe (e.g. Office International de l'Eau ). They present a challenge to hydrologists and hydraulic modellers to first identify the catchment processes that might be altered, and then to justify changes or 'shifts' to effective parameter values controlling these processes in their models.
NFM has often been seen as a low-cost alternative to traditional flood risk management techniques and is being Physics-based models can offer a useful lens for upscaling small-scale distributed processes such as increases in friction, storage and infiltration to study their combined effect at the catchment scale, yet also reveal a blurry image of our knowledge of exactly how to represent often variable and difficult-to-measure processes. The crux for modellers has therefore been how to represent very distributed and evidenced small-scale changes to hydraulic and hydrological processes, using efficient tools to capture the main interactions, whilst allowing for ensemble simulations and uncertainty estimation. Often a single type of model is used to represent the whole system, whereas using a combination of models (which are becoming more versatile to integrate) can improve the overall accuracy of process • Undertake cascade modelling of an ensemble of 'accepta- • Use more of the 2D modelling outputs to drive a better understanding of processes having a strong influence on flooding and flood risk reductionhere we use 2D depth and velocity data to estimate shear stresses and generate erodibility maps.

Study area and data
Swindale is a small, 15 km 2 upland valley near Shap in Cumbria, UK, with water draining from upland peatland cascading down to a valley with runoff characteristics dominated by impermeable glacial till. It has a high annual average rainfall   in an upslope HRU and be passed downslope to an HRU with a deficit and re-infiltrate. Here, we require a general NFM modelling framework that can represent such processes since these are processes that we seek to influence through, for instance, tree-planting or reduced grazing intensity. In the discussion we also demonstrate a similar coupling between Dynamic Top- In the discussion, we also compare the same approach to model integration using a combination of Dynamic Topmodel and HEC-RAS 2D (using a diffusion wave), using a much coarser resolution numeric grid (10 m).
We discuss how this scheme is able to incorporate detailed subgrid topographic data (2 m) despite the coarse grid (10 m), and explore additional outputs from the 2D hydrodynamic models, such as generating spatial distributions of shear stresses and erodibility maps.
These outputs can help understand sediment processes that are also important to understanding risk reduction and the long-term performance of RAF-based NFM measures, which may, if designed incorrectly fill up with sediment.   To show that the coupling Dynamic Topmodel with JFlow is a generic approach, we present a preliminary simulation of Dynamic Topmodel with an alternative 2D hydraulic model, namely, the licence-free HEC-RAS2D (https://www.hec. usace.army.mil/software/hec-ras/downloads.aspx). The HEC-RAS2D model has a new type of numerical scheme that permits efficiencies, whereby a relatively coarse numerical grid can be used (e.g. 10 m), for which the subgrid topography (2 m) is taken into account. This is achieved through precomputing hydraulic tables for each coarse numerical grid cell, comprising the conveyance across each face as a function of subgrid geometry, and then also a table of storage volume in the cell as a function of water elevation. This permits the modelling of channels that pass through the numerical cells if they are represented in the subgrid topography. Figure 7 shows the results of using HEC-RAS2D with a 10 m numeri- The approach yields very similar behaviour and performance at the gauge, and this increases confidence in the outputs from both models that either could be used in this model cascade approach.
To further illustrate the advantages of using 2d hydraulic models to better represent channel/floodplain flows resulting from the hillslope outputs Dynamic Topmodel, we very with Manning's roughness to estimate shear stress of the form where U is the depth-averaged velocity, d is the depth, and n  and very rough bed. Identifying such issues is critical to the design of NFM schemes and their long-term performance.

CONCLUSIONS
The study demonstrates the feasibility of utilising the best aspects of two models, using Dynamic Topmodel for hill-  We have demonstrated that the approach can be used for identifying the quantum of change due to an isolated runoff attenuation feature, and also the uncertainty associated with this, given as: 1.8 m 3 s À1 ± 1.4 m 3 s À1 . This represents a 4% ± 2% change at the flow gauge, which can help decision makers understand whether the intervention is worth investing in or re-engineering as a risk reduction strategy. In reality, further scenarios can be investigated, some diverting more of the flow from the main channel into Dodd Bottom, or through adding multiple features.
The approach will next be scaled up to the 210 km 2 Kent catchment, with 5 flow gauges and 72 km of watercourse as part of the NERC-funded Q-NFM project (https://www. lancaster.ac.uk/lec/sites/qnfm), to investigate the wider applicability of the approach. This larger catchment poses a computational problem, whereby it will no longer be feasible to simulate all of the behavioural Dynamic Topmodel scenarios using 2D hydraulic modelling at 2 m resolution, and a further sampling strategy will need to be devised.
Since many of the hydraulic outputs are similar, we intend to record statistics of each of the inflow time series from Dynamic Topmodel for each reach (such as peak, volume, time of peak) and use these to distinguish between scenarios likely to result in different spatial behaviours. These can then be further constrained with local knowledge of particular flooding pathways during recent flooding.