Uncertainty in Parameterizing Floodplain Forest Friction for Natural Flood Management, Using Remote Sensing

One potential Natural Flood Management (NFM) option is floodplain reforestation or manage existing riparian forests, with a view to increasing flow resistance and attenuate flood hydrographs. However, the effectiveness of floodplain forests as resistance agents, during different magnitude overbank floods, has yet to be appropriately parameterized for hydraulic models. Remote sensing offers high-resolution datasets capable of characterizing vegetation structure from a variety of platforms, but they contain uncertainty. For the first time, we demonstrate uncertainty propagation in remote sensing derivations of complex vegetation structure through roughness prediction and floodplain flow for extreme flows and different forest types (young and old Poplar plantations, young and old Pine plantations, and an unmanaged riparian forest). The lowest uncertainties resulted from terrestrial and airborne lidar, where airborne lidar is currently best at defining canopy leaf area, but more research is needed to determine wood area. Mean literature uncertainties in stem density, trunk diameter, wood, and leaf area indices (20, 10, 30, 20%, respectively) resulted in a combined Manning’s n uncertainty from 11–13% to 11–17% at 2 m to 8 m flow depths. This equates to 7–8% roughness uncertainty per 10% combined forest structure uncertainty. Individually, stem density and trunk diameter uncertainties resulted in the largest Manning’s n uncertainty at all flow depths, especially for flow though Pine plantations. For deeper flows, leaf and woody areas become much more important, especially for unmanaged riparian forests with low canopy morphology. Forest structure errors propagated to flow depth demonstrate that even small flows can change by a decimeter, while deeper flows can change by 40 cm or more. For flow depth, errors in canopy structure are deemed more severe in flows depths beyond 4–6 m. This study highlights the need for lower uncertainty in all forest structure components using remote sensing, to improve roughness parameterization and flood modeling for NFM.

determined the density of trees in stands of 500-1400 stems/ha with 6-34% uncertainty. High tree 145 detection uncertainties have also been determined from UAV lidar (e.g. [ Overall, the uncertainty range reported in the literature (Table 1) is 0-40% for stem spacing and 0-159 30% for trunk diameter. Average uncertainties are around 20% for stem spacing and 10% for trunk 160 diameter, when obtained using TLS and small footprint lidar.

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Terrestrial Laser Scanning is currently the most widely used remote sensing method in 163 determining real complex woody structure with centimetre-millimetre resolution. This is done through dual-wavelength TLS and subsequently removing the leaves through post-processing the point cloud.

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TLS has the ability to detect trunks, branches connected to trunks, and even lower order branches [36].

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It is noted that smaller branches can make a significant contribution to the total woody surface area

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In general, the uncertainty range from the literature (Table 2) are 0-30% for Leaf Area Index.

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Average uncertainties are around 20%, with low uncertainties for all remote sensing techniques 203 investigated, i.e. TLS, airborne lidar and radar.

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(2) The acceleration due to gravity (g) is 9.81 m/s 2 , and the slope of the channel (S) can be measured

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Wood Area Index for the forest types was determined from metabolic scaling theory. The 296 metabolic scaling theory, or West Brown Enquist model [116,117] is based on determining woody 297 structure from branch (RB), diameter (RD) and length (RL) ratios between mother and daughter 298 branches, which for conifers is defined as RB =5; RD = RB -0.5 ; RL=RB -1/3 , and for deciduous trees RB =3. For

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Using equations 1-3, Manning's n is calculated using the control forest structure described above.

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The drag coefficients for woody and leaf area ( , and , ), can either be determined using

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The unmanaged riparian site and the old poplar plantation increase in Manning's n uncertainty to ~10% at 8m flow depth at 40% WAI uncertainty. These two forest types have the highest WAI (WAI = 0.917-413 1.361), and so are expected to have the largest roughness sensitivity to changes in woody area.

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Uncertainty in estimated LAI also results in increasing roughness uncertainty at deeper flows 415 ( Figure 2). LAI uncertainties of 10, 20, and 30% results in average uncertainty in Manning's n by 0.9, 416 1.8, 2.7% respectively at 8m flow depth with less than 0.25% for 2m flow depths (averages include pine 417 plantations). As with WAI, LAI for the poplar plantations and the unmanaged riparian forest started 418 from within the first few meters. The unmanaged riparian site had a larger LAI than the old poplar 419 plantation (5.306 vs 3.997) and a canopy that started within the first 2m of tree height. This resulted in 420 roughness being 3 times more sensitive to changes in LAI between the unmanaged riparian and the old 421 poplar plantation.   Table S1).

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Propagating uncertainties in the species-specific drag coefficient (Cdi) and the species-specific 448 deformation parameter (χi) up to 50% to roughness are provided in the supplementary Figure S1.

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The uncertainty in discharge, propagated from uncertainty in roughness, increases from around 467 10% to 12%, 13%, and 13.5 % at 2, 4, 6, and 8 m flow depths (~45, 115, 195, 315 m 3 s -1 ) at the Avon river 468 cross-section (Figure 4d). The uncertainty in discharge over the generic floodplain (Fig 4j) increased 469 similarly from around 11.5% to 12.5%, 13.5%, and 14% at 2, 4, 6, and 8 m flow depths (~120, 255, 400,  and Poplar Plantations (Fig 4d,j). The relative uncertainty is opposite, with the highest discharge     sensing instruments -terrestrial and small-footprint airborne lidar -with campaigns in both winter 515 and summer. Here, stem spacing using TLS, small footprint and large footprint lidar report similar 516 uncertainties of up to 35% (Table 1). Trunk diameters should be monitored from TLS with multiple 517 scans, with uncertainties of 4-20% (Table 1). Small-footprint lidar can estimate trunk diameters to 518 similar levels of uncertainty (5-23%), although cannot readily detect smaller trunk diameters of 519 understory trees. The vertical distribution of branches should be determined using TLS (Table 2). Yet, 520 future work on scanning winter forests could determine vertical wood area indices using airborne lidar 521 [e.g. 84,101]. To determine leafy structure and LAI, small-footprint airborne lidar is best with 522 uncertainties of around 6-30% (Table 2). In this case, TLS is worse that small and large-footprint lidar 523 in detecting leafy structure, with uncertainty of up to 45%. If a single instrument is used for all four 524 forest structure components, then TLS will produce the lowest uncertainty for all components except 525 LAI, although LAI uncertainty offers the lowest change in Manning's n uncertainty (see Figure 3). Using 526 small-footprint airborne lidar only, will improve leaf area estimations, will maintain similar uncertainty 527 for stem spacing and trunk diameter, but may increase uncertainty for the branch components (see 528   Table 2). An effective magnitude of this increase in uncertainty cannot be given due to the lack of ALS 529 studies deriving branching structure.

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Uncertainty in Manning's n is smaller than any of the individual forest structure components 531 ( Figure 2 & 3), with uncertainty in deriving stem density and DBH contributing the largest uncertainty 532 to calculating Manning's n (10% uncertainty in stem density and DBH resulted in ~4.2% and ~3.5% 533 uncertainty in roughness respectively). For more extreme flow entering the canopy, the uncertainty in 534 defining WAI and LAI become more important, resulting in uncertainty to calculating Manning's n by 535 up to 2.6% and 2.9% per 10% uncertainty increase in WAI and LAI. For these reasons, improving remote 536 sensing methods that estimate trunk diameter and stem spacing should be prioritized over canopy 537 structure, in floodplains with a likelihood of low flood depths. For larger flood depths, TLS and 538 airborne lidar should be used to reduce errors in estimating woody and leafy structure. Of course, this 539 also depends on the type of forest (see next paragraph). Uncertainty in Manning's n is also smaller than 540 the combined forest structure components (Figure 3), where a 10% increase in combined forest structure 541 uncertainty results in Manning's n uncertainty of 7-8% (See also supplementary Table S1).

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River re-naturalisation is currently being promoted by the UK-Government through Natural

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England and the Environment Agency to create an interconnected channel and floodplain system that 544 serves both flood defence and biodiversity targets through the enhancement of natural processes. One  Figure 1 shows that older and denser 559 plantations offered 30% more resistance in the first 2 m flow depths than younger and sparser 560 plantations. Roughness of older plantations are up to 5% more sensitive to uncertainty in stem density 561 and DBH than young plantations, but up to 4.6% and 1.8% less sensitive to uncertainty in WAI and LAI 562 than young plantations (Figure 2). Therefore, deriving lower uncertainty stem density and DBH is more 563 important for older forest plantations, while deriving lower uncertainty WAI and LAI is more 564 important for younger plantations due to their lower canopies (Figure 1). Second, forests with lower 565 canopies (e.g. the unmanaged riparian forest) offer more resistance than forests with higher canopies 566 (e.g. old plantations), and uncertainties in WAI and LAI result in higher roughness uncertainties in 567 lower than higher canopies. The unmanaged forest has higher LAI and WAI than the old plantations 568 resulting in (see Figure 1) in up to 12% higher sensitivities to LAI and WAI uncertainties at 8 m flow 569 depth ( Figure 2). Third, poplar or other deciduous plantations have higher Manning's n than pines, 570 most notably when floodwater exceeds 6m in flow depth (Figure 1 bottom panel). This is again due to 571 woody and leafy area beginning lower in the canopy for poplars.

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A source of error that has not been discussed in this study is that of determining forest types.

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Estimating forest types is needed to calculate local and reach-scale frontal area and friction factors (Eq