Quantifying hydraulic roughness in a riparian forest using a drag force‐based method

Flow resistance through riparian forests due to drag on trees is often expressed in hydraulic models with an increase in a boundary resistance factor such as Manning's n. However, when Manning's n is used as a proxy for vegetation drag, this parameter is dependent on flow conditions and a single, uniform value may be inadequate for simulating a broad range of flood magnitudes. To investigate this issue, flow resistance, and the commensurate Manning's n values through a riparian forest were computed using measured drag forces and estimates of the forest structure and tree morphology. The computed Manning's n values were applied to a 2D hydraulic model (TUFLOW) to simulate an observed flood and a range of design floods. Modelled peak flood levels for the observed flood were 0.16 m lower on average than that recorded at debris marks. There was little difference in modelled flood levels when using the computed Manning's n compared to a traditional, uniform Manning's n. Reassuringly, the traditional method appears adequate when reliable calibration data is available. Otherwise, the method developed here provides a useful alternative in cases where calibration data is limited or for testing reforestation as a nature‐based solution in river or flood management.


| INTRODUCTION
To manage flood risk, it is necessary to understand the spatial distribution of the risk for a range of flood magnitudes from frequent to rare events. This is often done using hydraulic models to simulate historic and design floods along the river under consideration. The models are then used to inform and appraise potential management options, which may include structural measures such as levees or river diversions, or non-structural measures such as building controls or emergency and evacuation planning (Tariq et al., 2020). Where floodplains are wooded, the model needs to simulate the hydraulic roughness caused by tree drag. Traditional methods for selecting hydraulic roughness parameters, such as Manning's n, rely on lookup tables (Chow, 1959) and/or experience in a range of floodplain environments. Model results and roughness parameters are then verified against or calibrated to streamflow and other records from historic floods (Babister & Barton, 2012). Petryk and Bosmajian (1975) proposed a drag force-based method to determine Manning's n through channels with emergent vegetation using a description of vegetation drag. They used the classic drag force formula shown in Equation (1), where F D is the drag force, C D is an empirical drag coefficient (approximately unity for rigid smooth cylinders), A is a reference area of the object and U the flow velocity.
Their method balanced the downslope weight component of water against vegetation drag and bed shear stress. This approach is well established for the component of flow within the vegetation and has been used in several studies (Baptist et al., 2007;James et al., 2004;Luhar & Nepf, 2013;Stone & Shen, 2002;Yang & Choi, 2010). These studies differ in the treatment of vertical momentum transfer and variations in streamwise velocity near the canopy crown and above the canopy in the submerged case, which is not relevant for mature forests where flow depths are unlikely to rise above the canopy.
Equation (1) was developed for rigid objects. However, vegetation is flexible and the stems and foliage can reconfigure when loaded by drag forces. When vegetation reconfigures, a power drag-velocity law (F D / U 2þχ ) provides a better description of drag forces, where χ is an empirical parameter referred to as the Vogel exponent (Järvelä, 2004;Västilä et al., 2013;Vogel, 1984;Whittaker et al., 2013;Whittaker et al., 2015). Järvelä (2004) was the first to propose a drag model for woody vegetation that accounts for reconfiguration using a Vogel exponent. A dimensionless velocity term (U=U χ ) was used, where a normalising velocity (U χ ), which was needed for dimensional homogeneity, was arbitrarily assigned as the lowest velocity in the set of measured drag forces used to parameterise the model. A variant of the Järvelä (2004) formulation is shown in Equation (2), where A h ð Þ is the representative area of the tree exposed to flow at depth, h, and C Dχ is a speciesspecific drag coefficient. Järvelä (2004) used leaf area as the representative area, which can be normalised by the bed area to give the Leaf Area Index (LAI). Since LAI is used broadly in the environmental sciences, several methods have been developed to estimate this index (Antonarakis et al., 2010). Measurements of LAI can then be used to estimate spatial variations in tree drag and flow resistance in forests at field scale. Frontal area is also often used as a reference area for drag on vegetation (Jalonen & Järvelä, 2014;Västilä et al., 2013;Whittaker et al., 2015) and is used here along with estimates of tree frontal area from allometric equations and tree heights and densities measured from an aerial laser scanning survey.
Some tree drag measurements indicate the presence of an initial rigid regime where drag forces are too weak to induce stem reconfiguration and F D / U 2 as per Equation (1) Whittaker et al., 2015;Xavier, 2009). At higher flow depths and velocities, stronger drag forces induce stem reconfiguration and F D / U 2þχ as per Equation (2). This dual regime phenomenon can be simulated using a Cauchy number in the drag equation Whittaker et al., 2013;Whittaker et al., 2015). The Cauchy number is a dimensionless number that was introduced in the field of fluid mechanics and is defined as the ratio between inertial and compressibility forces in a flow. This number is also used to study fluid-structure interactions, for which it can be defined as shown in Equation (3) (Leclercq & De Langre, 2016;Luhar & Nepf, 2013;. The rigid regime occurs when the Cauchy number is <1 and the reconfiguration regime occurs when the Cauchy number is >1.  used the Cauchy number to redefine U χ in Equation (2) as a transition velocity separating the rigid and reconfiguration regimes. U χ can be determined from Equation (4), where Z h ð Þ is the first moment of frontal area at depth, h, and EI is a reference rigidity for the tree.
The two regimes are then modelled by placing limits on U χ , such that U=U χ is greater than unity in the reconfiguration regime and limited to unity in the rigid regime, as shown in Equation (5).
In practice, Manning's n is often applied as a single, uniform value. However, in forests Manning's n is dependent on flow conditions and increases as flow depths rise causing deeper inundation of the trees (Baptist et al., 2007;James et al., 2004). Also, the blockage of flow area and displacement of water caused by the stems and foliage is often ignored in flood simulations (Green, 2005;Nikora et al., 2008). Vegetation drag-based methods that account for the dependence of Manning's n on flow conditions have been tested in hydraulic models (Wang & Zhang, 2019). Some of the tested methods ignore reconfiguration (Baptist et al., 2007) and the tested methods that include reconfiguration ignore blockage (Järvelä, 2004;Whittaker et al., 2015). These studies do not explicitly investigate the deficiencies in using a uniform Manning's n in forests for design flood estimation.
The first aim of this paper is to develop a drag forcebased method to compute Manning's n in a forest using the tree drag model proposed by . The method, which includes reconfiguration and blockage in the analysis of Manning's n, is then tested in a depthaveraged 2D hydraulic model (TUFLOW) to simulate flow resistance through a riparian forest during floods. This study is the first to compute Manning's n in a sclerophyll forest using a drag force model with parameters that were calibrated to drag force measurements on sclerophyllous trees. The second aim of this paper is to compare the method against a uniform Manning's n approach to investigate the benefit gained in terms of improving the accuracy of flood level predictions for design flood estimation.

| STUDY AREA
The study area is located in southeast Queensland, Australia, in a rural upper reach of the North Pine River ( Figure 1). As for rivers elsewhere in the region, the alluvial morphostratigraphy is flood-dominated, reflecting the seasonally variable flow and large flood range of this subtropical region (Croke et al., 2016;Fielding et al., 1999;Kemp et al., 2015;. The main channel of the North Pine is compound in form (sensu Graf, 1988), and includes a low-flow channel with a bed gradient of 0.002. The channel is 30 m wide as it enters the site. The high banks then broaden and a narrow low-flow channel forms abruptly near the apex of the main bend. At this bend, a large point bar has formed on the convex bank featuring a scrolled pattern formed by groves of trees that are separated by flood chutes up to 1.5 m deep. Bed sediments are comprised of cobbles and sand grading up to fine sandy silt. Terror's Creek (Figure 1) enters the floodplain of the North Pine from the north and joins the larger river at a shallow angle near the tail of the main bend. The floodplain is dominated by two species of sheoak, which is an important riparian genus in Australia either in single genus stands or mixed with other riparian trees, typically broad-leaf evergreens such as Eucalyptus sp. River sheoak (Casuarina cunninghamiana Miq) and Swamp sheoak (Casuarina glauca Sieber ex Spreng.) have similar morphologies, being mostly single-trunked with a pyramidal canopy form and needle-like foliage. Both can function as riparian pioneers in disturbed floodplains, channel banks and low-lying bars because they can tolerate regular, deep inundation (Erskine et al., 2009;Woolfrey & Ladd, 2001). In the North Pine study area, F I G U R E 1 Site layout with geomorphology based on 2009 aerial photography obtained from the Department of Natural Resources, Mines and Energy (2020), which has adjusted since this date. The query point indicates the location for the hydrograph plotted in Figure 6b. river sheoak (C. cunninghamiana) makes up the majority of the forest (Figure 2). Patches of young swamp sheoak (C. glauca) appear on the bank of the low-flow channel and low-lying longitudinal bars. The sheoak forest extends approximately 700 m along the southern bank of the low-flow channel and extends up the floodplain of Terror's Creek (Figure 2).
The North Pine floodplain experiences deep inundations from the passage of tropical cyclones that stray southward on irregular but recurring periods. In January 2011, the stagnation of Ex-Tropical Cyclone Tasha produced an extreme flood with a peak discharge at the site of 1930 m 3 /s (estimated from rainfall records and modelling). Downstream of Lake Samsonvale, the return period of the January 2011 flood was estimated to be 500 years . The January 2011 flood impacted the riparian forest and low-flow channel alignment, stripping out trees and reworking the channel bars. Native broadleaf forest was planted on the higher floodplain following another large flood in January 2013 to reduce floodplain erosion in these catastrophic, but frequent, floods.

| Forest flow resistance
The effect of flow blockage and volume displacement caused by stems and foliage were accounted for using a volume reduction factor θ v and a flow area reduction factor θ a . These factors were estimated using tree frontal areas, assuming this area is symmetrical about the vertical axis. The average condensed tree diameter was estimated as A h ð Þ=h and the blockage factors computed using the footprint of the trees as shown in Equations (6) and (7).
The confounding effects of area blockage and volume displacement are combined using the θ term shown in Equation (8).
F I G U R E 2 Photographs at the study area showing (a) sheoak trees lining the southern bank of the North Pine River upstream of the point bar (taken from the opposite bank pointing in a southeast direction), (b) the lower trunks of the sheoak trees in the forest on the point bar, and (c) several sheoak trees.
The formulations developed in this paper ignore friction on sidewalls because the work is applied to a depthaveraged 2D hydraulic model. Thus, the hydraulic radius is h 1À θ a ð Þ. A more complete formulation of the hydraulic radius would remove the footprint of the trunk on the bed. For simplicity, this detail has been neglected as its contribution to flow resistance is considered insignificant. The force balance shown in Equation (9) is used to develop the forest flow resistance model, where S is the hydraulic energy slope, ρ is the water density and g is gravitational acceleration.
This equation balances the downstream component of a unit of water's weight against the total resistance from small roughness elements on the forest floor, τ 0 , and the resistance from tree drag per unit area τ 00 . Flow volume displacement from the tree stems and foliage is also included using θ v . The description of τ 0 , shown in Equation (10), is obtained by combining the Manning's and reach-averaged shear stress equations, where n 0 is the Manning's n representative of friction from small roughness elements on the forest floor.
For the description of τ 00 , velocity-specific drag is defined as F v ¼ F D =U 2 . Then, τ 00 is obtained by summing drag on each tree from i ¼ 1 to m in the forest and dividing by the forest floor area (A f ) as shown in Equation (11), and Equation (12) is used to compute the velocity-specific drag for each tree.
Equation (11) can be applied directly within the momentum balance equations solved by hydraulic models (Wilson et al., 2006). However, the more common method used here is to compute a composite friction parameter representative of overall resistance through the forest. Inserting Equations (11) and (10) into Equation (9) yields the relationship between velocity and hydraulic energy slope shown in Equation (13), where F R is a composite resistance factor, shown in Equation (14).
Finally, Equations (15) and (16) are obtained by rearranging the terms and applying Manning's equation n ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n 02 þ n 002 p ð15Þ Equation (16) is easier to solve in the rigid regime where it is explicit. However, this equation becomes implicit in the reconfiguration regime because here n 00 ¼ f U ð Þ and U ¼ f n 00 ð Þ. Thus, an initial check can be performed by assuming the rigid condition and calculating U with U=U χ ¼ 1. Then if U < U χ , flow is in the rigid regime and the solution is valid. Given the flow retardance caused by forest stands, a rigid drag regime may be common in mature forests where trees are much taller than the flow depth. This is explored further in the case study below. Equations (13) and (15) were solved for steady uniform flow through the forest for a range of flow depths and energy slopes using the 2009 ALS analysis of the forest structure (see Supporting Information). It was assumed that the trees are evenly distributed and the forest floor is on a uniform slope with n 0 of 0.045. For the drag force parameters, a C Dχ of 0.120 and χ of À0.876 was used, and to compute U χ , a rigidity, EI ¼ 2:44H 3:67 .

| Hydraulic modelling
A depth-averaged 2D hydraulic model was developed using TUFLOW's HPC fixed grid solver version 2018-03-AE (BMT, 2018). This solver uses a second order explicit finite volume scheme to solve the shallow water equations using an adaptive timestep and was developed to parallelise across thousands of computational cores to accelerate simulations running on graphics cards (GPU) (Collecutt & Syme, 2017). The underlying equations solved are the same as that solved by TUFLOW's Classic solver, which uses the Smagorinsky formulation to resolve the momentum diffusion term . Inflows were obtained from Moreton Bay Regional Council's regional rainfall-runoff model that had been developed using the software package, WBNM (Boyd et al., 1996;WorleyParsons, 2012). The WBNM model estimates discharge through the North Pine River and its tributaries during the January 2011 flood using recorded rainfall from 11 rainfall stations surrounding the catchment (see Supporting Information). The upstream and downstream boundaries in the TUFLOW model were positioned 1.4 km and 4.5 km from the study area, respectively. The peak flood level at the downstream boundary of the model was set to 41.99 m above Australian Height Datum (AHD, which is based on mean sea levels recorded between 1966 and 1968 using 30 tide gauges along the Australian coast) to match the peak flood level at the corresponding location in Council's regional TUFOW model. A flood level versus time hydrograph was developed for the downstream boundary condition assuming uniform flow at the boundary. Further details and a sensitivity analysis on the boundary are provided in Supplementary Information. The DEM developed from the 2009 ALS survey was used to configure the TUFLOW model topography. Bridge and culvert dimensions, as well as additional bathymetric data, were sourced from Council's regional TUFLOW model (WorleyParsons, 2012). Outside the study area, Manning's n values were initially set to match the regional model. Manning's n values downstream from the study area were adjusted to 0.045, 0.08 and 0.1 for pasture/ grassland, medium dense and dense forest to reduce the difference between modelled and recorded flood levels at the Dayboro stream gauge (station ID: 540484, see Figure 5) (Seqwater, 2020). Flood levels in the study area were not sensitive to these Manning's n adjustments. Within the study area, Manning's n values were determined from the flow resistance analysis in this paper. Peak flood level records from seven debris marks were captured by Council using a Trimble R10 GNSS receiver to a required accuracy of ±50 mm (WorleyParsons, 2012). However, the accuracy of the debris marks in terms of capturing peak flood levels will be less (Parkes et al., 2013). These records were compared to modelled flood levels.
In addition to the January 2011 event, design floods were simulated using a six-hour storm duration (Pilgrim, 1987;WorleyParsons, 2012). Design flows were obtained from WBNM models (WorleyParsons, 2012) and used as upstream boundaries in the hydraulic model. As for January 2011, flood level versus time hydrographs were developed for the downstream boundary for each flood.

| Model scenarios
The January 2011 and design flood simulations were repeated for a range of model scenarios to investigate the model's sensitivity to different aspects of forest resistance (Table 1). The scenarios test the inclusion/exclusion of reconfiguration and blockages and the use of a traditional, fixed Manning's n versus a depth-varying Manning's n. The FULL scenario includes reconfiguration, the RIGID scenario ignores reconfiguration, the NBLK scenario ignores blockage effects, and the TRAD scenario uses a uniform Manning's n value. To account for reconfiguration, the depth-varying Manning's n curve in the rigid regime was scaled using a bulk reconfiguration factor for the forest. First, the RIGID scenario was simulated and tree-specific reconfiguration factors, U=U χ À Á χ , at the flood peak were computed and plotted against flood depth at each tree. The trend from this plot was used to develop a depth-varying reconfiguration factor for the forest. To check the accuracy of this method, the sum of all drag forces computed using bulk reconfiguration factors was compared to that using tree-specific reconfiguration factors at the flood peak.

| Forest flow resistance
The results of the uniform flow analysis, shown in Figure 3, demonstrate that forest resistance inhibits the usual tendency for depth-averaged flow velocity to increase as flow depth increases. Instead, above a depth of 1-2 m, the depth-averaged velocity reduces and is then held constant with flow depth unless the slope is steep enough to generate velocities that are in the reconfiguration regime. Velocities are generally too slow to initiate the reconfiguration regime with only the steepest energy slope investigated (0.004 m/m) crossing into the reconfiguration regime at a depth of approximately 10 m. Manning's n is independent of velocity and increases with flow depth along a near linear profile in the rigid regime (Figure 3b). At steeper energy slopes the higher velocity causes some trees to enter the reconfiguration regime and the Manning's n curve deviates from the rigid regime curve with smaller Manning's n values. Manning's n increases with unit flow (product of depth and velocity) in the rigid regime, but the slope flattens when reconfiguration occurs (Figure 3c). The volume and flow area reduction factors, θ v and θ a , were 0.349 and 0.591 for the average peak flood depth of 5.2 m during the January 2011 flood, and increased to a maximum of 0.443 and 0.666 at a depth of 8 m.
T A B L E 1 List of the scenarios that were modelled. For scenarios using blockages, a volume reduction factor (θ v ) of 0.349 was applied to the storage volume within, and a flow area reduction factor (θ a ) of 0.591 to the flow areas across, the computational elements coinciding with the forest in the 2D hydraulic model. These values were based on the average peak flood depth in the forest of 5.2 m.

| Hydraulic modelling
Results from the FULL scenario (Table 1) suggest that 53% of the flooded trees in the forest were in the rigid regime and 61% had a reconfiguration factor at the flood peak, U=U χ À Á χ , of greater than 0.9. Thus, a little over half the trees were in or near the rigid regime at the flood peak. Shorter trees experienced greater reconfiguration. For example, the average height of trees with reconfiguration factors of less than 0.5 (9% of the forest) is 8.7 m, which is nearly half the average tree height of 16.0 m. Reconfiguration only occurred when flood depths were higher than 3 m. Ignoring reconfiguration (RIGID) resulted in a 19% overprediction of the total drag force through the forest. The Manning's n scaling used in the FULL scenario to account for reconfiguration (see Figure 4) reduced this overprediction to 2%. At the average peak flood depth in the forest of 5.2 m, the Manning's n reduced from 0.095 to 0.083 due to reconfiguration and increased to 0.13 when excluding both blockage (θ v and θ a of zero) and reconfiguration (NBLK). Peak flood levels estimated by the FULL scenario are compared with surveyed flood levels at the debris marks in Figure 5, which show a modelled flood level that is 0.16 m ± 0.13 m lower than recorded on average (using standard deviation to represent departure from the mean). These differences are not necessarily indicative of inaccuracies in the drag force-based method, and could have several sources including the records themselves, gaps in rainfall records or other modelling factors. Excluding reconfiguration increased levels at the debris marks by 0.02 m on average (RIGID À FULL). Removing reconfiguration and blockage factors caused a 0.16 m drop in flood level (NBLK À FULL) and removing both drag forces and blockage caused a 0.58 m drop in flood level on average (NONE À FULL). Thus, blockages accounted for approximately 25% of the increase in flood level caused by the forest. A comparison of the model results with flood level records at the Dayboro gauge is shown in Figure 6a. A bank failure at 9:00 am caused the sensor to malfunction and it was not possible to compare peak modelled and recorded flood levels at the gauge. On the rising limb of the hydrograph, before 9:00 am, modelled flood levels reach 0.33 m higher than recorded. Alternatively, the modelled rising limb occurs 15 min earlier than recorded. There is little difference in modelled flood levels at the gauge for scenarios FULL, RIGID and NBLK (Figure 6). Thus, the adopted forest flow resistance parameters only affected flood levels within and upstream of the forest. However, removing any representation of the forest resistance (NONE) resulted in a 0.43 m increase in peak flood levels at the gauge due to the loss of flood attenuation upstream (Figure 6b).
Averaged design event flood levels at the debris marks are shown in Figure 7a. The 200-year and 500-year flood levels for the FULL scenario are 48.71 m and 49.11 m above AHD, respectively. The average January 2011 flood level at the debris marks is 48.72 m. Given the model under prediction of 0.16 m, it is reasonable to estimate a $300-year return period for the January 2011 flood, which is lower than the 500-year return period estimated further downstream . Using the FULL scenario results for the January 2011 flood as a baseline, a uniform Manning's n of 0.17 was calibrated to match average peak flood levels at the debris marks and adopted for the TRAD scenario. Flood levels at the debris marks for the FULL and TRAD scenarios were similar with <0.01 m difference for events ≥200 years (Figure 7). The largest variation was for the 10-year event, which was 0.03 m higher in the TRAD scenario. A slightly lower Manning's n of 0.162 re-calibrates the TRAD scenario to match the 10-year peak flood levels at the debris marks with that in the FULL scenario and was adopted for the TRAD 10Y scenario. Peak flood levels at the debris marks for the TRAD 10Y scenario are 0.02-0.03 m lower than the FULL scenario for design events of >100 years (Figure 7a,c). A hydrograph of modelled January 2011 flood levels at the bridge is shown in Figure 7b and difference in levels in Figure 7d. On the rising limb of the hydrograph, flood levels for the TRAD scenario are as much as 0.16 m higher than the FULL scenario. This difference is slightly smaller, at 0.14 m, for the TRAD 10Y scenario. During the flood peak the TRAD and FULL scenarios simulate similar flood levels with a difference of no more than 0.03 m, and this difference is slightly larger at 0.05 m for the TRAD 10Y scenario.
F I G U R E 4 Manning's n values used for the modelling scenarios plotted against flow depth (h).

| DISCUSSION
The drag force-based method that has been developed to estimate Manning's n values through deeply flooded and forested floodplains produced Manning's n values of 0.06 to 0.1 for a depth ranging between 2 m and 6 m. This is similar to that normally adopted for forested floodplains (Arcement & Schneider, 1989;Chow, 1959). Peak flood levels simulated by the hydraulic model using the drag forced-based Manning's n values were 0.16 m ± 0.13 m lower than recorded at the debris marks, on average. This is a reasonable comparison given typical calibration tolerances of around 0.3 m for debris marks (Babister & Barton, 2012) and given the deep flooding with average flood depths of 5 m in the forest. Thus, the drag force-based method is considered to have performed well for the case study presented. While only one validation event has been investigated, this outcome is considered significant given that the data used to calibrate the drag modelling are independent from the flood event data.
The sensitivity of peak flood levels to inclusion/ exclusion of reconfiguration and blockage has been tested. The simulated January 2011 peak flood levels at the debris marks were only slightly sensitive to the inclusion of reconfiguration, which reduced peak flood levels at the debris marks by 0.02 m, on average. This is a minor change relative to the accuracy of the hydraulic model. Part of the reason for the low sensitivity to reconfiguration is that much of the forest remained in the rigid regime. Exclusion of blockage factors made a more F I G U R E 5 Comparison of modelled and recorded flood levels in metres AHD at the debris marks for the FULL scenario in the map and all scenarios averaged across the debris marks in the box plot. noticeable difference to peak flood levels at the debris marks, causing a 0.16 m average drop in peak flood level at the debris marks. Blockage contributed 25% of peak flood level rises caused by the forest. Other studies have found flow depth sensitivity to reconfiguration and blockage factors to be small (James et al., 2004;Wang & Zhang, 2019), which may be why some drag force-based methods ignore blockage (Baptist et al., 2007;Järvelä, 2004;Whittaker et al., 2013). These sensitivities will depend on forest maturity, since reconfiguration will be more pronounced in younger forests where the smaller trees have lower rigidity and a greater proportion of their stems and foliage exposed to flow. Also, younger forests are more dense than mature forests and are likely to cause greater blockage in floodplains (Yoda, 1963). The fact that Manning's n is not uniform in forests is well-known in the flood modelling community. However, a uniform Manning's n is often applied in flood models for practicality and due to a lack of generally accepted and easily applied guidance on how to vary Manning's n in forests. This study provides some insight into the nature and size of errors arising from the use of a simple, uniform Manning's n in design flood estimation. The uniform Manning's n calibrated to match peak flood levels during the January 2011 flood and the drag-force based method simulated peak flood levels similar to that Flood levels for (a) the design flood events averaged across the seven debris marks and (b) the January 2011 flood at the upstream face of the road crossing near the entrance to the study area (see query point location in Figure 1). Model scenarios are described in Table 1. The differences in flood levels between the TRAD and FULL scenarios and TRAD 10Y and FULL scenarios at the debris marks is shown in (c) and at the upstream face of the road crossing is shown in (d).
recorded. Therefore, the uniform Manning's n method appears to work as well as the drag force-based method for estimating peak levels when good quality calibration data is available; i.e. having a good quantity and spread of accurate records obtained during large floods that occurred at a time when forest conditions were similar to that being simulated for the design events (Ball et al., 2019). The drag force-based method will be useful in recourse when calibration data is limited. The drag force-based method also offers an improved approach for calibrating to the hydrograph shape. On the rising limb of the January 2011 hydrograph the uniform Manning's n simulated flood levels that were up to 0.16 m lower than the drag force-based method upstream of the bridge near the entrance to the study area. This is because the uniform Manning's n is calibrated to simulate the flood peak rather than lower food levels earlier in the flood event, and the uniform Manning's n overestimates forest resistance on the rising limb of the flood. The drag forcebased method can also be used to provide a check on calibrated Manning's n values which may be distorted to compensate for other modelling problems such as flow inaccuracies introduced by deficiencies in rainfall records or inaccuracies in the rainfall-runoff modelling. The data used here to develop models and calibrate model parameters is specific to sheoak forests. Canopy forms and foliage morphology for other species will differ, which will influence the drag forces and flow resistance accordingly. Therefore, to extend the drag-force based model to a broader range of forest assemblages including mixed-species forests in Australia and elsewhere, similar analyses will be needed on other species to derive model parameters. Sheoak morphology is relatively simple, consistent, and as an evergreen tree, seasonally unchanging. For species with less consistent canopy configurations, errors in generalised allometric relationships will be larger. Trees that are deciduous will require allometric relationships covering the phases of seasonal growth and dormancy. Grazing of low foliage and branches is another complication that has been observed in the field. While the parameters for the method developed here are limited to sheoak trees, the method can be applied more generally in future as the required parameters become available in the literature for other species. These parameters are currently available for a limited number of tree species (Whittaker et al., 2015;Xavier, 2009).
The resistance model developed here does not include a drag decay factor for wake sheltering by other trees. Thus, the approach may become inaccurate in dense forests where wake sheltering becomes more problematic. The average spacing of the trees was estimated to be 2.7 m. Based on rigid cylinder studies (Etminan et al., 2017;Nepf, 2011) and a study measuring velocity recovery in the wake of a real tree (Schleiss et al., 2014), this spacing is sparse enough to suggest minimal wake sheltering. However, the canopies are broader than the rigid cylinders and are porous media. Wakes behind porous objects differ to that behind solid objects, with wake zones that appear to be longer (Zong & Nepf, 2012). Also, reconfiguration and movement of the canopy due to the stems and foliage being flexible are likely to influence the structure of the wake. The canopy density will become compressed and the shape of the canopy will become more streamlined as flow velocities increase. The canopy will also move in concert with, and may dampen, pressure oscillations caused by vortex shedding in the wake zone, as was observed in the experiments of Sharpe et al. (2019) and  where vibrations on aluminium poles were not present when using trees. Further research on wake closure behind mature trees is needed to improve our understanding on wake sheltering in forests. Nevertheless, exclusion of wake sheltering seems adequate in this case given that model results were similar to recorded flood levels.
Understorey shrubs, herbs and grasses are also a source of flow resistance, and experiments suggest that large undergrowth relative to the primary storey can have a substantial influence on vegetation roughness (Berends et al., 2020). The influence of undergrowth will depend on its cross-sectional area relative to the primary storey and the flow depth (Carling et al., 2020). In the sheoak forest studied here, the undergrowth grasses and sedges, for which the resistance was simulated with a uniform Manning's n of 0.045, were highly flexible and were short compared to the flood depths and tree heights. Thus, tree drag was likely the main source of flow resistance through the sheoak forest. In smaller floods that manifest broad areas of shallow flood depths in the forest, roughness from the undergrowth may be more important.
The forest was estimated to increase peak flood levels by 0.58 m at the debris marks upstream and reduce peak flood levels by 0.43 m at the stream gauge downstream of the forest. The drop in flood level downstream of the forest is indicative of how forests can reduce flood risk to downstream communities (Brown et al., 2018;Lane, 2017;Nilsson et al., 2018). This research, and the methods developed here, may be useful for improving the accuracy of modelling used to analyse the effects of natural flood management and other nature-based solutions to river corridor management that involve largescale tree planting and/or riparian rehabilitation. Further to this, the drag force-based method is well suited to estimating how changes in forest height and density will influence flow resistance and flood behaviour over time as a forest matures.

| CONCLUSION
Manning's n values estimated from the uniform flow analysis increased with flow depth in the rigid regime, where Manning's n was independent of flow velocity. Flood depth dependence weakened in the reconfiguration regime where Manning's n reduces with increasing velocity due to weakening drag forces as the tree reconfigures and becomes more streamlined. Using the Manning's n curve to simulate the January 2011 flood in a 2D hydraulic model resulted in a 0.16 m under prediction of peak flood levels at seven debris marks, on average. A little over half the trees in the forest were within or near the rigid regime at the flood peak, and there was little change in flood levels when reconfiguration was included. At the debris marks, blockage factors accounted for 25% of the rise in flood level caused by the forest. There were marginal differences in flood levels using the traditional and drag force-based methods to determine Manning's n. Thus, the traditional method appears adequate when good calibration data is available. The drag force-based method improves the accuracy of the flood level hydrograph, provides a method to check calibrated Manning's n values, and may be useful in situations when calibration data is limited or when predicting forest roughness for natural flood management and river rehabilitation schemes.

NOTATION
A frontal area (m 2 ) A h ð Þ frontal area at depth, h (m 2 ) A f forest floor area (m 2 ) C D drag coefficient C Dχ species-specific drag coefficient EI reference rigidity (Nm 2 ) F D drag force (N) F v velocity-specific drag (Ns 2 /m 4 ) F v h ð Þ velocity-specific drag at depth, h (Ns 2 /m 4 ) F R composite forest resistance factor g gravitational acceleration (m 2 /s) h flow depth (m) i tree i in the forest from 1 to m m total number of trees in the forest n Manning's n n 0 forest floor Manning's n n 00 tree drag Manning's n S hydraulic energy slope (m/m) U flow velocity (m/s) U χ transition or normalising velocity (m/s) U χ h ð Þ transition velocity at depth, h (m/s) Z h ð Þ first moment of area at depth, h (m 2 ) ρ density of water (kg/m 3 ) χ Vogel exponent θ blockage term θ a flow area reduction factor θ v volume reduction factor τ 0 forest floor resistance (N/m 2 ) τ 00 resistance from tree drag per unit area (N/m 2 )