Strategies for Testing the Impact of Natural Flood Risk Management Measures

Natural Flood Management (NFM) is an approach that seeks to work with natural pro- cesses to enhance the flood regulating capacity of a catchment, whilst delivering a wide range of ecosystem services, from pollution assimilation to habitat creation and carbon storage. This chapter describes a tiered approach to NFM, commencing with strategic modelling to identify a range of NFM opportunities (tree-planting, distributed runoff attenuation features, and soil structure improvements), and their potential benefits, before engagement with catchment partners, and prioritisation of areas for more detailed hydrological modelling and uncertainty analysis. NFM measures pose some fundamen tal challenges in modelling their contribution to flood risk management because they are often highly distributed, can influence multiple catchment processes, and evidence for their effectiveness at the large scale is uncertain. This demands we model the ‘upstream’ in more detail so that we can assess the effectiveness of many small-scale changes at the large-scale. We demonstrate an approach to address these challenges employing the fast, high resolution, fully-distributed inundation model JFLOW, and visualisation of potential benefits in map form. These are used to engage catchment managers who can prioritise areas for potential deployment of NFM measures, where more detailed model - ling may be targeted. We then demonstrate a framework applying the semi-distributed Dynamic TOPMODEL in which uncertainty plays an integral role in the decision-making process.


Introduction
Natural Flood Management (NFM), commonly referred to in the UK as Working with Natural Processes (WWNP), has been defined as taking action to manage flood risk by protecting, restoring and emulating the natural regulating function of catchments, rivers, floodplains and coasts [1]. NFM can integrate improvements to the local landscape and ecology, thereby contributing to meeting environmental goals (such as European Water Framework Directive objectives). Compared to hard-engineered Flood Risk Management (FRM), NFM is becoming attractive to policy makers and catchment managers due to lower upfront costs, the potential to create multiple ecosystem benefits (e.g. carbon storage, diffuse pollution and sediment risk regulation), and for its flexible scale of deployment, which may also help to stimulate or encourage community involvement. The mechanisms to achieve such aims include run-off storage, increasing soil infiltration, slowing surface water movement and reducing flow connectivity.
Across a catchment, there can be many different opportunities for NFM such as upland mire restoration, revised/modified land management and land use, woodland creation, sediment management, built water storage, river restoration and development of Runoff Attenuation Features (RAFs) to intercept overland flow. The key characteristics shared by these measures are that they are typically small-scale and highly distributed, and potentially alter a wide range of catchment processes. As a consequence of their small scale and local impact, they are mostly likely to be effective in reducing downstream flooding when implemented widely in the headwaters of catchments to reduce streamflow reaching downstream floodplains. Catchment models routinely applied by regulatory agencies and water authorities for flood risk assessments, forecasting, water resources planning or water quality management, tend to represent upstream areas as discrete sub-catchments with uniform inputs. This can be very effective for simulating flows in the river further downstream near urban settlements, but averages over the effects of small-scale interventions and thus loses information into their impacts on the various hydrological processes of interest. For highly distributed, smaller scale measures and interventions, it will be vital to consider new approaches that not only scale their impact up more accurately but also consider the uncertainty in the representation of how catchment processes might change. There are still large evidence gaps and a need to test the effectiveness of these distributed measures against observational data. This will require detailed monitoring of catchment processes. A recent survey [2], however, showed that as few as 6% of NFM schemes in the UK have intensive hydrological monitoring.
The approaches demonstrated here aim to address the scaling-up problem in a way that reflects the uncertainty in the representation of small-scale hydrological processes and flood mitigation methods. In doing so we meet the challenge that was put to environmental modellers by Beven in 2009 [3], to give decision makers:

'…a realistic evaluation of uncertainty since this might actually change the decision that is made'
By means of an example, we examine here a tiered approach taken to planning NFM strategies within the headwaters of the Eden, Kent and Derwent catchments in Cumbria, UK (Figure 1), that aimed to prioritise where different measures are likely to be most effective.
This was followed by an analysis of uncertainty in the environmental model parameters and of the fuzziness in the evidence behind the changes applied to these models to represent effects of NFM measures.
We show how the effectiveness of very distributed NFM measures such as tree planting and enhanced storage in the headwater catchments can be appraised in a framework similar to established FRM practice. Advances in high-resolution modelling (here we explicitly model runoff on a 2 × 2m resolution grid within a 100-million-cell model [4]), have unlocked the potential to model 'upstream' at high resolution, and enable us to test the aggregated impacts of very small scale measures at the larger scale. This delivers a deeper understanding of the effectiveness of potential NFM plans in reducing peak runoff, but requires new strategies to consider 'synchronisation' issues [5], whereby flooding can be made worse by slowing the time of arrival of a flood peak in one tributary such that it interferes constructively with that of the receiving watercourse. It also opens up the ability to undertake continuous modelling through sequences of events, such that the antecedent wetness is taken into account.
Since NFM measures could be deployed in very many spatial configurations, it follows we should test for synchronisation effects against a wide range of plausible extreme loading conditions. The authors demonstrated such an approach in a recent UK government Flood Modelling Competition, where their winning entry [6], combined high resolution modelling of NFM with advancements in spatial joint probability analysis of extremes [7,8], whereby multiple extreme rainfall scenarios were simulated, with realistic spatial patterns based on the long-term records at rainfall gauges around the catchment. The 'average' effectiveness of NFM across the upper part of the 2,300km 2 Eden catchment was then tested against 30 simulated extreme rainfall events selected to span a range of spatial patterns.   Figure 2 highlights a pathway through the risk management cycle that attempts to integrate core elements needed for modern flood risk management, adapted for NFM with its distinguishing features of highly distributed interventions and uncertain impacts. This framework was developed and applied in the course of the Cumbrian project for identification of the types of NFM opportunities introduced earlier, with whole catchment modelling being applied to map potential risk reduction benefits.

A risk management framework for NFM
This first step was undertaken for the Cumbrian project using rapid overland flow modelling approach using a 2 m resolution 2d JFLOW model to identify where modification of features in the landscape to slow and store surface water flows might make the most difference. These included the use of RAFs at locations of high flow accumulation, tree-planting, and soil structure improvements. The speed of set-up, very high resolution and rapid run times of JFLOW meant we were able to rapidly assess the effectiveness of these very distributed NFM measures, before sharing with catchment partners.
Our work in Cumbria has involved a wide range of catchment partners including landowners, flood management agencies, voluntary groups and farming groups, who used the whole-catchment mapping to refine potential opportunities for NFM deployments and also prioritise areas for more detailed modelling. The sub-catchments containing the most promising opportunities Flood Risk Management based on the JFLOW modelling were prioritised for more detailed uncertainty investigation using Dynamic TOPMODEL [9,10] to compute the projected benefits of NFM.
Dynamic TOPMODEL provides a tool to help understand the effects of NFM on the total hydrograph, including contributions from overland flow and subsurface flow. The detailed models were calibrated against observed data collected during the period November-December 2015, in order to capture the flows arising from a sequence of prolonged and intense rainfall events associated with Storms Abigail and Barney prior to the most severe storm, Desmond (4-6 December 2015), which led to extreme rainfall and flooding in Cumbria [11,12].
An uncertainty framework was used to represent not only the uncertainties in the parameters used in the model but also the gaps in the scientific evidence on how different NFM measures influence catchment processes (Figure 3). A large number of simulations were undertaken for each catchment, and a set of model parameterizations showing 'acceptable' performance on the basis of the evidence, were identified based on a range of measures including the ability of the models to reproduce the observed peak flow for Storm Desmond.
The next sections cover the broad steps in this flow chart.

Evidence for effectiveness of NFM
This section reviews evidence of the effects of NFM on catchment processes, and how this evidence was mapped onto the effective parameters that are used in the different modelling strategies adopted in the Cumbrian opportunity mapping project. This section gives a flavour of how we gathered evidence of changes to physical processes in the UK and tried to map these changes onto already uncertainly modelled processes.
For the JFLOW overland flow modelling, the physical influences considered were: • Increasing roughness through land cover changes: grasses and mosses to shrubs and trees • Increasing localised depression storage through construction of RAFs • Increasing infiltration through improvements in soil structure For Dynamic TOPMODEL, we consider the above processes and also those influencing subsurface flow, for example: • Reducing surface overland flow velocities through woodland planting.
• Increasing surface storage associated with RAFs using modified surface routing and a maximum storage parameter.
• Increasing soil transmissivity through woodland planting.
• Increasing wet canopy evaporation through woodland planting.
The evidence for the above changes linked to tree-planting was considered with respect to deciduous woodland, which brings the most habitat and biodiversity benefits in this environment, and is in line with current activity within NFM schemes across the UK.

Surface roughness
Considering the roughness of the ground covered by improved pasture, heathland or deciduous woodland, many different elements combine to produce an effective roughness for a whole hillslope. Within a deciduous woodland, roughness contributions come from: (1) roughness of the litter layer, (2) roots at the ground surface running across the slope, (3) obstructions to flow caused by tree stems/understory, (4) paths and tracks, (5) fence lines or walls, and (6) subgrid topographic irregularities in slope. All components need to be characterised to provide an accurate measurement of the effective roughness of a whole hillslope. Direct measurements of the roughness components across a range of surface vegetation conditions at floodplain sites in Florida (USA) [13] produced Manning's n [14] values that ranged from 0.030 to 0.061 for forest areas against a range of 0.013-0.050 for other surfaces including barren land and grasslands.
Chow states that floodplains covered by pasture should be ascribed a roughness value of 0.035, while those covered by light brush and weeds 0.050, dense brush 0.070 and dense forest 0.1-0.2 [14]. Thus in direct comparison with the direct measurements of roughness undertaken in Ref. [13], the differences between woody vegetation and pasture-cum-barren land are considerably less. Given: (1) the limited number of studies directly measuring hillslope roughness [13], (2) the discrepancies between the field-measured and tabulated (or estimated) values, combined with (3) the large variability in roughness values measured even within the same vegetation types, a large uncertainty should be placed on the range of possible roughness values used in models.
In this study, a comparison is made between with and without woodland, that amounts to a maximum increase of 50% in Manning's roughness, over the broad-scale 'upland' roughness value of 0.1 used to provide national flood maps in the UK. Thus a maximum of 0.15 was used compatible with the engineering tables of Chow, but which requires more research to resolve the underlying physical processes contributing to frictional losses.

Peatland management
Similar issues arise when estimating the effects of peatland management on the effective roughness of hillslopes as with the comparisons between the effects of forest versus pasturelands. For example, peatland restoration may involve replacing patches of bare peat with Sphagnum spp. moss, changing micro-scale roughness, but also adding small obstructions within the artificial drains. Holden et al. [15] used 256 bounded overland flow plots (0.5 m x 6 m) in the Upper Wharfe catchment (UK) and found that the roughness was greater when Sphagnum spp. moss rather than bare ground was present, resulting in a reduction of overland flow speeds by a factor of 3.3. This equates to an increased roughness of ~0.3, which was used in the JFLOW modelling and the reduced wave speed in Dynamic TOPMLODEL, albeit starting from the relatively high generic roughness factor used in the national mapping, of 0.1 and increasing it to 0.13. Here we have used the roughness increase only, as the effect of drain blockage is not as clear and can be strongly dependent on the orientation of the drains, i.e. whether they run across slope or down slope [16].

Runoff attenuation features (RAFs)
Small ponds to capture and temporarily store overland flow on its way to stream channels have been described as 'overland flow interception RAFs' or 'overland flow disconnection ponds', where RAFs are 'runoff attenuation features'. Temporary storage of the overland flow on slopes could delay this component of the flow so that it reaches streams after the peak of the hydrograph has passed. However, if overland flow on a particular slope is generated on the rising stage of a stream hydrograph [17], delaying it could have the unwanted effect of adding the overland flow contribution to the channel at the time of the peak in the streamflow. Clearly understanding precisely when the overland flow is being added to stream channels, and doing so within a spatial frame of reference, is critical for understanding how it should be managed. Only a few direct measurements of overland flow using plot studies are available in the UK (e.g. Ref. [18]) to help quantify the timing of this process. The Belford Catchment Solutions Project in Northumberland has demonstrated how such features are able to retain and hence attenuate the initial phase of overland flow generation. Overland flow interception RAFs have been constructed at many locations in the UK and individually range from 20 to 1000 m 3 in capacity (see Refs. [19][20][21]). RAFs added into the simulations for this study are 100-5000 m 3 in area and so are broadly similar in capacity.

Wet-canopy evaporation
Deciduous woodlands in the early winter (i.e. November-December) in Western Europe, when the overstory is leafless, exhibit only very small rates of transpiration [22]. Potentially, these rates may be marginally higher than those for improved grasslands, if the woodland is open and accompanied by a leafed understory vegetation of shrubs and/or longer grasses [23][24][25][26]. This effect is, however, likely to be insignificant when compared with the contrasts in wet canopy evaporation (also called 'interception loss' or Ewc).
As Reynolds and Henderson [27] noted '…although sometimes there is a measurable reduction of interception losses in winter due to leaf fall, the effect is commonly surprisingly small…' Combined Ewc and transpiration losses from grasslands in the early winter are likely to be small, for example, 5.6% of gross rainfall (100 [16.3/289.5 mm] for months of December 1975-1985 [28]). However, in some contrast, the wet canopy evaporation rate for deciduous woodland when the overstory is leafless in winter is likely to be within the range 10-20% of the gross rainfall for the conditions prevailing in the UK or for similar situations in continental Europe ( Table 1), but perhaps less (as a percentage) for high magnitude events.  Table 1. A wet canopy evaporation range (over 1-3 months) that also encompasses most of the extremes in observed behaviour of leafless vegetation canopies would be 7-50% of gross rainfall through winter storms for deciduous trees, although likely to be at the lower for an extreme event so a range of 4-20% was used in the modelling. Table 1 was used to define the fuzzy set of wet canopy evaporation rates (top right panel of Figure 3) used in the Dynamic TOPMODEL but constrained to the smaller range of 4-20% considering the extreme nature of Desmond.

Antecedent moisture status
The higher rate of wet canopy evaporation during winter leafless periods, combined with the higher combined rates of wet canopy evaporation and transpiration from leafed deciduous trees in the proceeding summer and autumn in comparison to grassland [29][30][31], means that UK woodland soils are likely to be drier during the winter. A drier subsurface condition will reduce the proportion of rainfall delivering fast streamflow responses thereby reducing peak flood flows [32,33]. Finch [34] observed drier soil moisture profiles (by 250 mm) beneath sweet chestnut and larch woodland and grasslands in Pang basin (Berkshire, UK) through December in 1997. Indeed, the profile did not reach its maximum saturation until April 1998. Similarly, Calder et al. [35] show soil moisture deficits through December 2000 that are drier by 30 mm in the soil (0-0.90 m) beneath oak (Quercus robur L.) of Clipstone Forest (Nottinghamshire, UK) than beneath adjacent grassland. A scenario of 80 mm of additional soil moisture deficit beneath deciduous woodland compared to grassland in the early winter is within the 30-250 mm range of the two UK studies noted but is clearly associated with a highly uncertain range.
NFM might feasibly give wetter antecedent conditions in a sequence of winter events if the increased infiltration effects of tree planting on soil moisture are larger than those of enhanced wet canopy evaporation ('infiltration trade-off hypothesis'). Here we attempted to account for this through detailed modelling of several consecutive storms, and although the drier antecedent soil moisture was taken into account, the deficit was reduced considerably after the first storm in the series.

Woodland on slowly permeable, gleyed UK soils
Overland flow on hillslopes may be caused by rainfall intensities (mm/hr) exceeding the saturated hydraulic conductivity (K S ; mm/hr) of a topsoil or other surface horizon (equivalent to the 'infiltration capacity' or 'coefficient of permeability of the topsoil'). This rapid pathway of rainfall towards stream channels is called 'infiltration-excess overland flow' [36]. If rainfall is reaching the ground at a rate less than the saturated hydraulic conductivity of the topsoil, but cannot infiltrate because the topsoil is already saturated as a result of drainage from upslope areas, then the rainfall onto these saturated areas will move as overland flow across the surface. This pathway is called 'saturation overland flow by direct precipitation' or SOF by direct precipitation [37]. If the downslope subsurface flows exceed the ability of the downstream soils to discharge them directly into a stream channel, then subsurface water may emerge from the topsoil onto the ground surface as 'return flow' [38]. This return flow may then travel overland towards a stream as so-called 'saturation overland flow by return flow' (SOF by return flow).
Soil types that typically have a lower saturated hydraulic conductivity have a greater likelihood of generating 'infiltration-excess overland flow', and were present in downslope areas, also a greater likelihood of generating surface flows by 'saturation overland flow by direct precipitation' and 'saturation overland flow by return flow'. The soil type called a Gleysol using the international soil classification system [39] or gley within the Soil Survey of England and Wales (SSEW) soil classification system [40] typically exhibits lower saturated hydraulic conductivity values throughout UK soil profiles [41]. Table 2 shows an example K S profile for a gley in the Lune Valley, Northwest England (UK). These measurements were undertaken in the field with a ring permeameter [42], a technique demonstrated to give accurate values, even for disturbance-sensitive gley soils [43].
Soils in England and Wales that are classified as gley cover a range of soil associations based on the SSEW [44]. As a result of their greater likelihood of generating overland flow, these gley soils are classified as having an SPRHOST 1 value in excess of 50% [45]. Enhancing the permeability of such soils could have the greatest impact on reducing overland flow across catchments and thereby have the greatest potential to reduce flood peaks in rivers [46]. As a result, tree planting to increase soil permeability includes areas with such gley soils.
Consequently, for NFM modelling a key need is to represent the permeability effects of planting deciduous trees on gley soils. Very few UK studies are available that quantify the difference in soil Ks of gley soils beneath deciduous trees relative to that beneath adjacent grasslands [47].
These few studies are summarised in Table 3 and give a range of 1.5-3.5 factor increase in permeability for deciduous tree planting on gley soils. The Ks factors in the first column of Table 3 were then used to provide the fuzzy set of parameter changes in the Dynamic TOPMODEL scenarios.
This observed increase in permeability for gley is smaller than the factor of five difference between predominantly deciduous woodland and improved pasture recently observed on well drained Eutric Cambisol (SSEW Brown Earth) soils in Scotland by Archer et al. [48,49]. The observed effect on gley is also smaller than the effects observed on other soil types across the globe, the majority of which are between 2 and 20, with some outliers much greater than this, which is likely to be due to macropores along root channels. In any event, if the roughness of these high runoff areas can be increased through roughening up, then it may be possible to attenuate quick-flow from these soils until they become saturated by deficit filling.  Critically, it should be remembered that most of the stream hydrograph during floods comprises water that has primarily travelled to the stream via subsurface pathways (effects of trees on Ks might not be isotropic-but we have even less information on downslope Ks). Even within very flashy, but undisturbed tropical streams, only small proportions of flow within the basin have been directly measured as overland flow (e.g. <10% streamflow [50]). Therefore, while the overland flow pathways are important given their speed and sediment transport aspects, especially during flood events, simulated flow pathways are likely to be dominated by subsurface responses (which can also be fast-subsurface celerities in wet soils can even exceed overland flow velocities [51]), pathways either close to the surface in soils or deeper within the surficial or solid geology [52,53].

Opportunity mapping of NFM
Opportunity maps can be developed from local knowledge, land cover maps, flood modelling outputs, or a combination of all three, as described here. In this chapter, opportunities for three core types of NFM (tree-planting, RAFs and soil structure improvements) were developed from different national strategic maps, and then through consultation at an engagement event.
Ideally, engagement would be a continuous process of refinement where more local knowledge of the landscape and opportunities are built in through time, and evidence is co-produced [54]. The following sections explain how these opportunities were identified and refined.

Runoff attenuation features
Research on RAFs [55][56][57] such as storage ponds, bunds, in-stream storage through woody debris dams and disconnecting drain flow pathways has shown that these features have the potential to reduce flood peaks and increase the time to peak for overland flows and streamflows. Applying RAFs within the headwaters of a catchment, therefore, has the potential to attenuate sudden short duration storm events and reduce the subsequent flood risk to more urbanised areas of the catchment downstream.
Opportunities to deploy RAFs can be identified from areas of high flow accumulation in surface water flood maps, and comprise small areas such as natural depressions within the landscape, or small in-channel storage as shown in Figure 4. The JRAFF model identifies the Results of related study of Carroll et al. [81] rejected on basic quality assurance criteria (i.e. absent sampling size per land-cover; absent information on frequency distribution, etc.). orange areas of isolated flow accumulation, such as ponds and small channels, which may be appropriate to excavate or bund, or disconnect from flow pathways through gully or ditch blocking. An additional storage of 1 m in depth at these locations is represented through burning the Digital Terrain Model (DTM) deeper by 1 m in the RAF model scenario.
The JRAFF tool places a set of constraints on the size and location of these accumulations: • Area threshold between 100 and 5000 m 2 ○ This was considered suitable for local land management alterations, and well below the threshold of capacity that would fall under the UK Reservoirs Act (10,000 m 3 ).
• CORINE land cover 2012 dataset and a 2 m buffer of OS OpenData buildings and roads deemed unsuitable to runoff attenuation features.
○ A 2 m buffer of roads results in a 4 m wide exclusion zone. This threshold has been derived based on typical road widths and ensures that opportunity features within any potential adjacent ditches are retained.
In the application to Cumbrian catchments, the JRAFF model was used to calculate the additional storage volume if such areas were to be deepened 2 by a further 1 m before summarising 2 Equally representing a bund around an existing flow accumulation area these volumes within priority sub-catchments defined earlier. Within the Kent catchment only, any RAFs identified within peat soils were excluded where hillslopes were greater than six degrees. This constraint is based on current peat restoration practices [58]. This process identifies a very large number of opportunities which can be incorporated into a model. These opportunities represent large scale, long term NFM delivery and provide the evidence required to take a strategic approach to optimising the benefits of providing additional distributes storage within the catchment.

Identification of tree-planting opportunities
Restoring the riparian zone and planting woodland within the floodplain has been simulated to provide the potential for significant flood attenuation (see Refs. [59,60]). A combination of improvements in wet canopy evaporation and transpiration enhanced soil drying and soil infiltration together with increases in hydraulic roughness which arise from woodland creation can lead to reductions in flood peaks together with delaying and spreading of tributary hydrographs.
The Woodlands for Water (WfW) opportunity EA dataset was supplied by the Environment Agency for this project [61] and it was modified with the local knowledge and through inspecting soil series maps to give potential tree-planting opportunities (Figure 4). The dataset typically comprises a set of woodland plantings opportunity areas such as riparian zones and floodplain areas together with a number of constraints such as urban areas, existing woodland and inland water. Whilst the source dataset infers opportunities to plant and enhance woodland areas, this scenario rather reflects a more general improvement in planting density between scrubland and mature forest as it is understood that conversion to mature woodland would not be appropriate across all land covers.
The modified WfW opportunity maps represent large, long-term NFM delivery within each catchment. The incorporation of this opportunity into the model provides the evidence required to take a strategic approach to optimising the benefits of providing additional 'natural roughness' within the catchment.

Identification of opportunities for soil structure improvement
This scenario pertains to the fact that many soils have been compacted through more intensive farming practices over a long period of time, and if de-compacted, improved soil structure has potential to take in and store considerably more of the incident rainfall [62]. This can help reduce overland flow and reduce downstream flood risk, although could potentially have limited benefits in wet winters.
For the third type of opportunity, soil structure improvement, the JFLOW modelling targeted a particular land cover (improved grassland) which was identified as one of the most common land covers within each catchment based on the Land Cover Map 2007. For these areas, the catchment descriptor BFIHOST [45], which influences amount of runoff routed over the landscape in the modelling (see below), was increased by 10% resulting in an approximately equivalent increase in maximum soil moisture storage and reduction in initial soil moisture storage capacity for these land cover areas across the catchment. Users can then assess the improvement relative to that for this type of land cover by scaling up by relative area compared to improved grassland.
This more targeted approach to improving soil permeability avoids overestimating the impact of soil improvement by applying an unrealistic blanket improvement across the catchment. Soils can only be improved if they are damaged. Palmer and Smith, 2013 [63] estimated that approximately 38% of soils were structurally damaged, the percentage was higher under arable and lower under pasture, in a survey in the SW of England.

Strategic modelling and estimating benefits
The strategic modelling was undertaken using a fast 2d hydrodynamic modelling software JFLOW [4], which has been benchmarked against other 2d inundation models against a wide range of test cases [64]. The approach illustrated in Figure 5, builds on the blanket rainfall approach (e.g. Ref. [65]), which was developed further to include the ReFH losses model [66], and used to develop a national SW flood map RoFSW [67]).
The model integrates spatially varying rainfall, with the representation of both rural infiltrations using the ReFH rainfall to overland flow calculated losses (i.e. infiltration) model and urban sewer loss rates (a national average of 12 mm/hour was used). Rural ReFH losses are controlled by the maximum soil moisture storage capacity (Cmax) which is estimated using the catchment descriptors BFIHOST and PROPWET whilst urban losses are based on estimated sewer capacity losses and percentage overland flow. The floodplain is represented using a 2 m Digital Terrain Model (DTM) based on a combination of filtered LiDAR, filled in with coarser scale photogrammetry or SAR data. Sinks and dams are removed in order to maximise hydrological flow pathway continuity. Spatially varying hydraulic roughness coefficients were adopted throughout, based on land cover and the same roughness coefficients adopted in national maps. The baseline scenarios were for the 10-year and 30-year return periods with a 6-hour storm duration.
Much consideration is given to the placement of virtual monitoring locations around the catchment that monitor the hydrographs for different sub-catchments and their modelled response to NFM interventions (Figure 6). For urban areas, culverts and 'cut-throughs' can be added to allow the passage of water downstream more realistically.
The percentage change in the peak runoff response for each sub-catchment was then visualised in a second set of 'benefit maps' (Figure 7), for use at the engagement workshops. These were colour themed in different ways, with the perimeters shaded to reflect the magnitude of the modelled peak runoff reduction and the fill based on the extent of the opportunity. Benefits are cumulative, in that every opportunity must be implemented within upstream sub-catchments in order to obtain the visualised benefits.
These maps represent the potential benefits of large-scale, long term NFM delivery across a catchment. They are most appropriately used in relative mode, allowing the user to identify particular sub-catchments which provide greater benefit than other sub-catchments and the different interventions that should be targeted to provide these benefits.
Other approaches to showing benefits or damages avoided have been developed, whereby the average property damages [68] per 1 km tile are shown with and without NFM, and this  helps put appraisal of NFM on a footing with more established methods and identify potential dis-benefits due to, for example, backwater effects causing upstream flooding.

Engagement and refinement
Visualisations such as Figures 4, 7 and 8 have been found useful at engagement events, whereby catchment partners can mark the maps and alter the opportunities based on their local knowledge, then see the potential benefits based on the broad-scale modelling. Many of the identified opportunities will not be feasible due to land ownership and access issues. There may already be interventions planned which can also be added to the maps. Following the engagement, the models were re-run and the maps and interactive PDFs regenerated for the whole catchment.
One key benefit of the engagement approach is the development of a shared understanding of flood generation, routing and accumulation within a catchment. The opportunity for planners, water company engineers, land managers, FCRM, water quality and biodiversity specialists to elicit hydrological understanding from modellers including issues of synchronisation is of enormous value. The engagement process also enables the modelling team to appreciate and incorporate a more credible set of opportunities and parameters back into the model. This   two-way process builds confidence in the model outputs, allowing delivery organisations to make appropriate use of the modelling, based on improved understanding, as part of the weight of evidence required to develop a more strategic approach to NFM delivery.
In addition to the refinement of the opportunities, and through remodelling the benefits, the catchment partners were asked to prioritise sub-catchments for more detailed modelling to build confidence and implement NFM. A matrix was developed, based on the following criteria: • Land ownership and access-are opportunities feasible?
• Observations based on local knowledge • Observations from strategic maps

Modelling of NFM with dynamic TOPMODEL
Given limited observational evidence effectiveness of NFM at scales >10 km 2 , the prioritisation of areas to model in more detail and through using Monte-Carlo simulations was considered essential to understand more about uncertainty and build on the screening-level modelling with JFLOW (despite its high resolution). The detailed modelling was therefore calibrated against an observed series of extreme events, Nov-Dec 2015, within three severely-impacted catchments up to 223 km 2 in the area within Cumbria, UK. The results from one of these catchments, the upper Kent (90 km 2 ) are used in the following sections to illustrate the approach that was taken for all three catchments.
Lancaster University has recently developed an extended and flexible implementation of the Dynamic TOPMODEL model [9,10], first implemented in FORTRAN by Beven and Freer [9]. It is an extension of the popular TOPMODEL [69] applied in many studies [70]. Dynamic TOPMODEL employs the efficient parameterisation scheme of TOPMODEL, but allows a more general approach to a grouping of points in a catchment for calculation purposes, based on overlays of characteristics rather than simply the map of the topographic index.
All the model parameters needed to run the model are shown in Table 4, along with typical ranges of values applied in this project. Figure 9 provides a perceptual overview of Dynamic TOPMODEL.
It is a semi-distributed hydrological model that utilises areas of similar hydrological behaviour called HRUs (Hydrological Response Units). These units may be in the evaluation of NFM divided to represent distributed interventions within the landscape. It has sufficient complexity to represent the key catchment processes, notably subsurface and overland flow pathways, and there is some evidence to link NFM measures to alteration of the parameters (e.g. transmissivity  distribution) representing these processes. Its simple structure allows efficient operation, allowing thousands of model runs to be simulated to investigate uncertainties and sensitivities.
Overland flow velocity is fixed throughout each unit and can be changed to reflect changes in surface roughness introduced by, for example, peat restoration or riparian tree-planting. The maximum transmissivity at complete saturation T 0 [L] 2 /[T] is a measure of the local maximum saturated downslope transmissivity per unit hydraulic gradient (where transmissivity is the integral of the permeability to the saturated depth). This is a key parameter in identifying the onset of saturation overland flow (SOF). When downslope flows into lower slopes filling remaining storage capacity, return flow is produced. SOF is also generated when rain falls onto these areas of already saturated ground.
An exponential transmissivity profile is assumed. The use of such a form is supported by experimental evidence [71] and reproduces the typically higher values of permeability found near the ground surface. The recession parameter m [L] controls the rate of decline of transmissivity T as water table reduces. Small values of m lead to very rapid declines in transmissivity, suggesting shallower, faster responding streamflow generation systems. Deeper active hydrological systems are represented by a slower decline in transmissivity.
Dynamic TOPMODEL routes subsurface flow downslope between HRUs using a routing matrix derived from the local topography. It is assumed that the local slope is a reasonable approximation for the hydraulic gradient.
The root zone storage SRZ max must be filled before any water table recharge begins through incident rainfall. Transpiration (and soil evaporation) is removed from this zone at a rate proportional to the actual storage. Direct observations of soil moisture content are unavailable for the catchments in the periods simulated, so a reasonable initial value was applied (SRZ 0 = 95%). Dynamic TOPMODEL represents an intermediate level of complexity that incorporates the key hydrological processes, but without imposing too many assumptions resulting in a large number of parameters (related to say soil properties), for which we do not have direct measurements. The model was also selected because of it: • Makes use of standard data formats for catchment topography (elevations, channel network) and relevant spatial data such as land cover.
• Presents results back to the landscape as well as formats such as streamflow hydrographs that are easily understandable by partners.
• Uses real, spatially distributed rainfall data and can be rapidly calibrated against real event data (allowing for data quality).
• Incorporates spatial data overlays provided by the Rivers Trust (RT) and catchment partners of NFM interventions, for example, tree-planting, soil restoration and the addition of offline storage area (RAFs) and simulate the effect of these changes on streamflow response.
• Simulates a wide range of catchment scales (up to 223 km 2 in this study) and hydrological regimes such as the extreme flood event arising from Storm Desmond in December 2015.
• Allows for relatively quick application to future RT study catchments and different configurations of sub-catchments within an existing project.
• Uses a framework that allows assimilation of meteorological and streamflow data supplied in standard formats, such as those collected by the Environment Agency.
• Allows for free distribution of the source or compiled the code and, with suitable guidance and training, be operated by RT staff and catchment partners.
In conjunction with a hydraulic-routing scheme, also developed at Lancaster University, Dynamic TOPMODEL has been applied to the 28 km 2 Brompton, North Yorkshire, catchment in order to simulate the impact of up to 60 in-channel NFM interventions [5]. The model is written in the open source R language, distributed under the GNU Lesser Public Licence (GNU LGPL v2.1) and can be run on most common operating systems. The R implementation has been released as a package on the CRAN archive [72], passing the rigorous quality assurance and testing required by the submission process.

Representing NFM opportunities within HRUs for Dynamic TOPMODEL
A set of HRUs were developed based on local hydrological characteristics, the most important of which is the topographic wetness index (TWI). These were then split further so that individual NFM measures could be represented in the landscape. For example, the HRU representing the saturated area adjacent to the watercourse in the upper catchment becomes split into two, one where there is no change to the landscape and another where there is tree planting.
○ Decreased SOF velocity (reduced by 0.5 and 0.75-equivalent to a change in roughness for JFLOW).
○ Wet-canopy evaporation increases implemented as a loss to the gross rainfall input (using a similar strategy to Ref. [73]).
○ Modification of the initial root zone storage to mimic drier antecedent soil moisture conditions as a result of additional soil drying by enhanced wet-copy evaporation. ○ Implemented as the sensitivity of three pipe sizes to see differences in 'effective' size based on peak reduction.
• HRU3-Peat ○ Decreased SOF velocity (reduced by between 0.65 and 0.8-equivalent to a change in roughness implemented for JFLOW).

Uncertainty framework
The scale of the flooding caused by Storm Desmond is in part dependent on the catchment wetting from the storm events that occurred over the preceding weeks. In consequence, a 6-week period of rainfall and streamflow was selected in Nov-Dec 2015 (Figures 4-6) for the modelling, that included Storms Abigail (12-13th November), Barney (17-18th November), Clodagh (29th November) and Desmond (5-6th December). The first and last of these events had the highest impact on the streamflow. Clodagh was primarily a 'wind' storm and in Cumbria did not produce significant streamflow [11]. In November a south-westerly airflow described as an 'atmospheric river' became established bringing persistent warm moistureladen air from subtropical regions resulting in persistent heavy rainfall. A 3-day total of 138 mm was recorded at the Shap automatic weather station in mid-November [11], compared to the total of 145-180 mm recorded at rain gauges around the Kent catchment in September and October. Two gauges lying within the Derwent catchment recorded new UK record rainfall totals: at Honister Pass, 341 mm fell within 24 h and 405 mm within 48 h at Thirlmere [11]. Dynamic TOPMODEL requires as input a time series of potential (or actual) evapotranspiration. We used the Calder et al. [74] approximation of a diurnal sinusoidal variation in potential evapotranspiration.
5000 Monte-Carlo simulations were undertaken before applying an acceptability criterion which sorts behavioural simulations, from those that are not. Within the Generalised Likelihood Uncertainty Estimation framework (GLUE [75][76][77][78]), the degree of acceptance of any simulation is weighted (or scored) quantitatively and is associated with the simulation during the entire analysis. Any simulations which are deemed physically unacceptable play no further part in the analysis and do not form part of the results.
The acceptance criteria were based on an overall performance measure over the whole modelled period (the Nash-Sutcliffe Efficiency statistic, NSE), the accuracy of the model prediction for the peak flow Q max during Storm Desmond, and the maximum percentage of the catchment areas generating overland flow (by saturation through either of the processes described), SOF amax . Figure 10 illustrates the spread in model uncertainties through the calibration time series based on the resulting 'acceptable' parameter combinations.
Given the range of acceptable model predictions for each storm the problem arises of comparing the NFM interventions for all acceptable models. To compare the respective hydrographs contemporaneously is likely to be misleading, since each series' maxima may occur at different absolute times due, for example, to the retardation of the flood peak by the NFM measures. The distribution of flows for a window of time-steps around the peak has therefore been generated so that the shift in the distribution can be compared. This is illustrated in Figure 11.

Results and discussion: comparison of models
We present here mainly the results for the Kent catchment, where the acceptance criteria discussed above were: NSE > 0.85; 6.9 < Q max < 10.2; 0.1< SOF amax <0.95, where Q max is the peak flow per unit area for storm Desmond and SOF amax was the very fuzzy range of acceptable fractional catchment areas producing SOF. This lead to 348 'acceptable' parameterisations, giving a range of predictions shown in Figure 12, for the RAF measures, designed to have a 1, 10 and 100 h retention time.    Figure 13 shows the range of potential changes to the storm profile when we apply two different levels of confidence (1 and 5, with 5 the least confident) in the evidence for the effect that tree-planting has on the different catchment processes.
It easier to consider the range of predicted peak flow reductions for each storm as a function of the confidence we place in the evidence (Figure 14) than by plotting the five different levels of confidence.
We can also make use of the generic approach from Figure 11, and plot the matrix of changes to the predicted peak flow distributions for a window around each named storm as a function of confidence (rows) in Figure 15, with a statistical significance of the changes highlighted in Figure 13. Effect of tree-planting opportunities with two levels of confidence in parameter changes.    Table 5. The WfW scenarios 1-5 were simulated, where there is more confidence in the evidence for scenario 1, and scenario 5 is the least confident. All the changes are more significant for storm Desmond, and the changes due to the RAF measures are generally more significant than the WfW.
Using Dynamic TOPMODEL, we have modelled drain-down of RAFs successfully with different time constants, and shown that for the Kent, RAFs designed with an intermediate residence time of around 10 h would be more effective for a series of flood events such as those in the period November through December 2015. The percentage reductions in peak flows are similar to the 2-5% peak runoff reduction predicted by JFLOW (30 year event) for the upper Kent for most of the period of modelling, apart from storm Desmond where Figure 12 shows less reduction, potentially because the RAFs have not emptied.
It is less straightforward to compare the results for tree-planting between the modelling approaches, but for the Upper Kent, JFLOW predicts peak streamflow (without baseflow) reductions up to 30-40% for a 1 in 30 year design event (Figure 7), and based on Figure 14, the maximum reduction in total flow was half this, of the order 17% for storm Barney, but for simulations with the least confidence. However, these changes stem from very different physical processes, and further modelling has shown that although the perturbations applied to the wet canopy evaporation have the predominant impact, the combined effect was greater than the sum of the individual changes for evaporation, velocities and transmissivity.
The potential impact of large-scale NFM delivery on peak flow during extreme events such as storm Desmond is an important result. The evaluation of uncertainty enables us to use this finding appropriately and with greater confidence. The modelling allows us to see both the long-term potential of NFM and, critically, the model parameters and processes to which this prediction is most sensitive. These findings not only improve our understanding of the benefits of NFM but also guide future monitoring strategies that will be required to refine the modelling and adaptively manage NFM, and therefore flood risk, within a catchment. A consistent theme within the engagement was that it would be unlikely that advantage could be taken of every single potential opportunity, and so the results can seem overly optimistic but could be used in a relative sense. ∆q max = maximum relative reduction in peak (%); ¯ Δq = mean relative reduction in peak (%); K-S = Kolmogorov-Smirnov Statistic. The suffix to RAF corresponds to a retention time of 1, 10 and 100 h.

Testing resilience
These types of analyses provide us with more confidence in the predicted response of the upper Kent to large-scale interventions of tree-planting and RAFs, yet we have not fully tested the long-term robustness nor the resilience in the face of different weather extremes. It would, in fact, be useful to test for a number of performance issues in order to gain greater confidence in the approach. These issues include: • Synchronisation.
• Effect of sequences of events on antecedent conditions.
• Culvert or bridge blockage due to increased debris from tree-planting.
These can be examined and tested through modelling of extreme events with different spatial rainfall fields (especially for larger catchments) as performed for the Defra competition [6], for the Eden as shown in Figure 16.
Here the average beneficial effect of NFM across 30 extremes, but plausible, rainfall events was generated (Figure 17) in order to test for robustness in using such distributed events in the larger Eden catchment in Cumbria.
Ideally, the additional modes of failure of NFM should also be tested for through probabilistic modelling, as currently undertaken for established FRM in the UK. A systems-based approach could be applied [79] as discussed in relation to wider processes from synchronisation of flood peaks, backwater effects, sedimentation effects whereby RAFs fill in through time, and blockage of downstream features such as culverts near urban areas due to an increase in woody material in the longer term, although it is also important to re-think the implications of performance failure for very distributed small-scale measures, compared to established flood risk management approaches [80].

Conclusions
We have demonstrated a generic flood risk management framework that caters for the distinct differences between NFM and established approaches such as engineered downstream flood defences. NFM measures are characteristically small-scale and may need to be widely distributed to be effective at larger scales, and can influence a range of catchment processes. This combination means that modelling their effectiveness will be inherently uncertain, but we have demonstrated a framework that is tolerant of this uncertainty and the fuzziness in the evidence for how model 'effective' parameters can be plausibly changed to reflect their effect.
The tiered approach involves strategic modelling, mapping of opportunities and benefits, consultation and then prioritisation of areas for more detailed modelling and eventual implementation. The engagement phase is essential and ideally should be more of a continuous process through time with details of the model landscapes (topography, distributed roughness, storage, tree-cover, land-use), being revisited regularly. This is not new, but this chapter has hopefully shown how it can be achieved practically in the reasonable timescale of just 6 months.
However, differences in the model predictions from the different modelling approaches require careful interpretation and are only part of the picture set in the context of uncertainties on long-term ownership, maintenance and liabilities for NFM measures. The strategic overland flow process modelling is bound to lead to some different catchment responses than for a complete hydrological model, yet both shed light on different risk management issues. For example, the surface water modelling approach is useful for identifying key flow pathways and accumulations where partial blockage or storage can make a greater difference, but Dynamic TOPMODEL tells us more about the whole hydrograph and can integrate with more of the processes that tree planting is thought to influence. The two modelling strategies have helped to increase our knowledge of how and where in each catchment NFM measures can be more effective to reduce flood risk at large catchment scales. The models help shed more light on the complexities of parameterising change in model parameters, particularly at large catchment scales and for a range of flood events.
The potential for large-scale NFM delivery to provide significant flood risk benefits, even in extreme events, is based on a translation of the limited available evidence on the impacts of NFM between the 'real world' and the 'modelled world', using an uncertainty framework.
If we believe that the model is a reasonable physical simulator of the whole catchment, then the potential benefits of following the risk management framework demonstrated are to help express model outputs in a language which highlights uncertainties and makes them more central to decision-making.
The models have helped to quantify by how much working with natural processes can improve flood regulation, depending on a fuzzy evidence base. The associated benefits can then be appraised alongside others, including carbon storage or reductions in diffuse pollution, sediment transport and improved community resilience through working together. However, we must stress the need for more information on the way in which model parameters might change as a result of land management changes as the information currently available is limited, in particular in respect of the type of flood event conditions relevant to NFM.