*2.2. Field Data Collection*

Field observations were collected during two experiments conducted in November 2016 in the southern Firth of Thames and in April 2017 in the Pahoia sub-estuary of Tauranga Harbor. In each case, arrays of water level sensors were deployed, along with RTK-GPS surveying and manual vegetation surveys. Details of surveys and deployments are given below.

#### 2.2.1. Vegetation Survey

Vegetation surveys were conducted to quantify the rigid vegetation at the study sites. The heterogeneous distribution of vegetation, large study area, and diverse mangrove properties necessitated a unique approach to measure vegetation. The survey objective was targeted at the two types of structure that characterize the flow-reducing properties of *Avicennia marina*: (1) The pneumatophores and seedling which comprise small, but dense structures near the seabed and (2) the trees and branches which are much less dense but can form a large blocking mechanism at high tide and surge levels. Flexible leafy canopies were not quantified. Mangrove canopies in the Firth of Thames were at sufficient elevation to not submerge and therefore did not influence flow resistance and were not quantified. The shrubby mangroves at Pahoia were submerged at high tide (Figure 7). Attempts were made to quantify canopies in Tauranga using the structure from motion, but were unsuccessful due to the difficulty of gridding the complex leaf geometry. Therefore, the leaves and small branches will provide an unquantified additional blocking. Visual observations indicated that flows were not sufficiently strong to cause the flexing of the leafy vegetation.

Due to the different growth forms of the mangroves at the two sites, slightly different strategies were employed. In the Firth of Thames, mangrove trees in some areas were nearly impenetrable, 5 m by 5 m quadrats were established along the cross-shore instrument transect. In Pahoia, where the mangroves were generally less than a meter tall, a cross-shore and an along-shore transect were established, and vegetation properties measured every 10 m.

In the Firth of Thames, the number of trees was counted in each quadrat. The height and width of the canopy and the stem diameter at 0.3 m from the seabed were manually measured for 5 trees closest to the pre-defined coordinates within the quadrat. To quantify pneumatophores, five 0.5 by 0.5 m quadrats were selected, one at each corner and one at the center of the large quadrat. Within these small quadrats, all the pneumatophores and seedlings were counted. In addition, the height, top diameter, and bottom diameter of five pneumatophores were measured resulting in a total of 25 pneumatophores measured at each station (Table 3).

In Pahoia, a transect through the central mangrove forest was established. Along the transect, the canopy height was measured at 5 m intervals. Pneumatophore and seedling characteristics were measured in 0.5 by 0.5 m quadrats every 5 m using the same method as that used at the Firth of Thames site. Pneumatophore statistics in Table 4 are based on the measurement of 5 pencil roots.

The vegetation drag is estimated as proportional to vegetation frontal area [30]. The frontal area (*av*) assumes that both the trunks and pneumatophores are rigid emergent vegetation (*av* = *nd*) where *n* is vegetation element density and *d* is the average diameter. Note that the contribution of pneumatophores to the total frontal area is reduced when water levels fully submerge the pneumatophores. The direct measurement of trunks in the Firth of Thames was used to generate the frontal area parameter. The complex configuration of plants in Tauranga (Figure 7a) made the measurement of trunks problematic. Therefore, general relationships between trunk density and canopy height, as well as trunk diameter and canopy height, were obtained for the vegetation data in the Firth of Thames. Assuming that the general structural properties of New Zealand *Avicennia* growth forms are the same between sites, these relationships were used to estimate the trunk density and diameter for Tauranga based on local measured canopy height. This method generates values for frontal area density (with uncertainty because of the assumptions of similarities between sites).

#### 2.2.2. Bathymetry

Manual RTK GPS surveys were conducted to obtain bathymetry at both study sites. In the Firth of Thames, an RTK survey of the instrument transect was conducted using a Trimble R8 GNSS system (Figure 3a). In Tauranga, RTK elevations were obtained for the western channel and a transect through the central mangrove forest (Figure 3b) with a Leica GS18 T GNSS system. Additionally, LIDAR data was provided by local government organizations for both sites (Figure 6). All elevation surveys were initiated and terminated with verification of vertical measurement accuracy with a fixed survey mark, the measurement error never exceeded 3 cm.

#### 2.2.3. Water Level

Pressure sensors were deployed at each of the study locations (Figure 2, Tables 1 and 2). The array of water level sensors deployed in the Firth of Thames in November 2016 consisted of a single transect of 9 instruments, extending from the stopbank to the mudflat (Figure 2a): Station 1 was seaward of the vegetation on the mudflat, stations 2–5 were located across the sloping forest region and stations 6–9 were spread across the forest platform (Figure 3a). A man-made channel is located just seaward of the stopbank and is evident in the transect survey (Figure 3a). At PAHOIA in Tauranga, the central mangrove forest and both the east and west channels were instrumented with pressure gauges (Figure 2b). Station #A is at the seaward edge of the mangroves and at the intersection of the two primary channels. Three stations (#B, #E, and #H) were located at increasing distances into the vegetated intertidal platform. An additional two gauges were positioned in each of the two channels.

Pressure sensors were corrected for variations in barometric pressure and for temperature dependence and referenced to mean sea level using survey data. Pressure signals were smoothed using a low-pass filter and converted to the water level using a constant water density of 1025 kg/m3.


**Table 1.** The Firth of Thames instrument array. Note that during factory calibration, the Aquadopp depth uncertainty over the range of interest was <5 cm and the Vector uncertainty was <2 cm.



#### **3. Results**

Water levels across the Firth of Thames and Pahoia study sites for successive tidal cycles are displayed in Figure 5. The ~1 km wide mangrove forest in the Firth of Thames site reduced the peak water levels and delayed the inundation signal, with the reduction and delay increasing with distance into the forest. The largest inundation wave in the Firth of Thames reached a maximum of 72 cm above the tidal flat at the seaward forest fringe and decayed to 53 cm above the tidal flat at the landward most station. This water height reduction of 19 cm across the 800 m separation between station 1 and station 9 corresponds to a dissipation rate of ~24 cm/km. The temporal delay in peak water between station 1 and 9 is evident in Figure 5 and estimated at 60 ± 5 min. The average velocity of peak inundation through the Firth of Thames mangrove forest is ~0.2 m/s.

At the Pahoia site, no measurable reduction in water level occurred over the ~1 km separation between instruments. The dissipation of flood levels was less than the uncertainty of the elevation measurements. Additionally, no identifiable temporal delay in peak water occurred over the study site (Figure 5c,d).

The magnitudes of the inundation waves for the two locations are similar with respect to the elevation of the mangrove forest. The inundation waves for both sites range from ~20 to ~70 cm above the average forest elevation (Figure 8). Nonetheless, the elevation of inundation relative to MSL was different between the two sites (Figure 5), with the Firth of Thames ranging from ~220 to ~245 cm above MSL at the seaward boundary of the mangrove forest, while the Tauranga inundation wave varied between 80 and 125 cm above the MSL.

**Figure 8.** (**a**) The peak water level at each instrument station along the transect in the Firth of Thames for 5 consecutive inundation events; (**b**) the peak water level at each instrument along the central mangrove transect in Tauranga (#A, #B, #E, and #H). Elevations are with respect to average elevation of the forest floor, profiles of which are shown in grey.







#### **4. Discussion**

Mangroves reduce peak water levels during a flood by limiting the exchange of water through the vegetation [18]. Krauss et al. [15] observed that the presence of channels decreased the efficacy of mangrove flood attenuation from 9.4 cm/km to 4.2 cm/km. Using a combination of observations and numerical simulations, Zhang et al. [16] found that the amplitude of storm surge was reduced at a rate of 40–50 cm/km through mangrove forests and ~20 cm/km through patchy regions consisting of a combination of mangrove islands and open water. Flood level reduction during the series of large inundation events in the non-channelized Firth of Thames averaged 24 cm/km, which agrees with rates previously published for unchannelized forests by Krauss et al. and Zhang et al. [15,16]. In contrast, the channelized New Zealand mangrove site in Tauranga had no measurable reduction of flood amplitude. We statistically tested whether tree height and pneumatophore density, diameter and height differed between sites. Because the raw (and transformed) data did not meet the assumptions of normality (Shapiro-Wilk W test *p* < 0.001) and/or homogeneity of variances (Levene's test *p* < 0.01) required for t-tests of differences between means, we used the non-parametric Mann-Whitney U test (a = 0.05). All statistical analyses were conducted in Statistica version 13.2. The results indicated that tree height, pneumatophore density, and pneumatophore height were all significantly different (*p* < 0.001). As a consequence, the frontal area, and therefore the flow resistance, from trunks was greater in Tauranga than in the Firth of Thames (Tables 3 and 4). Additionally, Chen et al. [31] demonstrate that mangrove canopies only increase the generation of turbulent kinetic energy by about 10% compared to when the flow is below the bottom of the leaf structures. Despite flow engagement of the dense leafy canopy in Tauranga (Figure 7d), the vegetation had no flood mitigating influence due to preferential routing through the channels.

The interaction of water and vegetation is complex and has been investigated at multiple length scales. At small scales (O (mm)), the boundary layers and shear caused by individual stems, roots, and leaves cause turbulent eddies that shed off each individual stem [32]. Turbulence is also generated at the shear layer between the faster moving flow over submerged vegetation, and the damped flow within the canopy [33]. Intermediate scales (O (m)) comprise flow at the canopy or patch scale involving a community of vegetation. Larger length scale interactions (O (km)) occurs at the forest level [34]. To appropriately investigate a process of interest, a reasonable spatial scale, associated conceptual model, and relevant measurements and methods must be identified [21]. Vegetated regions produce high drag with respect to unvegetated areas and flow is diverted to the path of least resistance. In areas described as dense vegetation patches, most flow is directed around the patches and a forest-wide approach is required. In sparse or homogeneously distributed vegetation, smaller-scale resistance dominates and a smaller-scale approach is justified [35].

In mangrove forests, it is not just the vegetation geometry that controls water transport, the intertidal bathymetry, and water level relative to the elevation of the vegetation also play a role [36–38]. Flow through mangrove forests has been categorized into creek flow or sheet flow depending on the primary mechanism of fluid transport. Creek flow dominates in channelized mangroves at low water levels. Sheet flow, the transportation over the vegetated platform through the mangroves, becomes increasingly important with reduced channelization and at increasing water levels [36]. Our results show that the Tauranga mangrove forest is dominated by creek flow, and the density of mangrove vegetation therefore only has minimal contribution to the flow restriction; no evidence of reduced inundation level nor delay in the flood signal exists. In Tauranga, flow resistance is best described by the larger-scale distribution of vegetation and degree of channelization. Conversely, the Firth of Thames mangrove forest is not channelized, and the primary shoreward water transportation mechanism is sheet flow through the vegetation. Here, vegetation properties are important for impeding water exchange across the forest, reducing inundation levels and slowing the flood wave propagation. In the Firth of Thames, the flow resistance relates to the vegetation properties along the one-dimensional cross-shore transect. The cumulative influence of large quantities of individual stems, stalks, and leaves on fluid flows at forest wide scales necessitates

simplifying vegetation summary statistics [20]. Several different statistical parameters have been used to describe the influence of vegetation on large-scale flow resistance, including the solid volume fraction, vegetation porosity, and frontal area per bed area [21].

Channelization in mangrove environments develops as the trees grow and create flow resistance and concentrate the flow into channels [3]. However, for initiation of the feedback process that allows the channels to develop, the intertidal platform must be at a sufficiently low elevation with respect to the tidal excursion that currents occur on the vegetated platform. In the case of a very high platform, inundation only occurs at slack water close to high tide, at which time conditions promote sediment deposition. The Tauranga mangrove forest is inundated during normal tidal levels. The drainage channels in the Tauranga study site have likely resulted from scouring by tidally-driven water transport through the forest. The forest elevation in the Firth of Thames is higher than the Mean High Water Spring (MHWS) water levels (Figure 3a) and therefore water is only infrequently transported through the forest and channels cannot develop.

During the study, water depths in the relatively flat mangrove forests in Tauranga and the Firth of Thames were of similar magnitude (Figure 8). The capacity of mangroves to provide coastal flood protection is ultimately related to water transport pathways. Extrapolating from our case study environments, we can expect that lower intertidal areas with channelization will be far less capable of protection than higher intertidal areas with little channelization. Krauss et al. [15] and Zhang et al. (2012) found that the reduction of flood levels along a river corridor was less than through unchannelized vegetation but still provided flood protection. Both previous investigations focused on hurricane-driven storm surges in the south-east United States. The extreme water levels greatly exceeded the capacity of the channel networks, likely resulting in flow pathways through the vegetation and therefore the capacity to mitigate flood levels was apparent but reduced compared to unchannelized locations. Moreover, the sediment regime has been shown to contribute to the development of a profile shape, with muddy profiles often associated with high convex intertidal geometries [39].

#### **5. Conclusions**

The influence of mangroves on long wave propagation is strongly dependent on flow routing. In highly channelized mangrove forests, such as our Tauranga case study area, water is preferentially transported via the channels and flood levels are not reduced substantially across the forest. In these cases, the vegetation does not contribute significantly to flow resistance, so specific plant properties are irrelevant with respect to limiting fluid transport. However, we hypothesize that for sufficiently large flood events, in which the conveyance capacity of the channels is exceeded, a proportion of the flow will be forced through the vegetation, which will thus provide an intermediate level of attenuation (still reduced relative to an unchannelized environment). Conversely, in homogeneously vegetated forests without channels, such as the Firth of Thames study site, water is transported through the mangroves and the trees reduce flood levels by limiting fluid exchange through the forest. In these cases, knowledge of vegetation characteristics is essential for the prediction of the rate of flood level reduction.

The degree of channelization and therefore the capacity of mangroves to reduce flooding depends on the elevation of the vegetation. Mangrove forests that occur at relatively low, frequently inundated elevations are subjected to tidal currents that promote channelization, which in turn reduces their capacity to mitigate the flood water level. Higher elevation mangrove forests are inundated only at the peak tide when currents are at a minimum and the sediment regime is depositional. No channel network is created nor maintained, and the capacity of the mangrove forest to reduce flood events is maximized.

**Author Contributions:** Conceptualization, J.M.M. and K.R.B.; Methodology, J.M.M., K.R.B., E.M.H. and J.C.M.; Formal Analysis, J.M.M.; Data Curation, J.M.M., and E.M.H.; Writing-Original Draft Preparation, J.M.M. & K.R.B.; Writing-Review & Editing, J.M.M., K.R.B., E.M.H. and J.C.M.; Funding Acquisition, K.R.B. and J.C.M.

**Funding:** This research was funded by the Natural Hazards Platform program (contract C05X0907) AND THE Royal Society Marsden Fund (grant 14-UOW-011).

**Acknowledgments:** The authors gratefully acknowledge the field help provided by Dean Sandwell, Heide Friedrich, Caitlyn Gillard, Hieu Nguyen, Dave Culliford, and Rex Fairweather. Help with statistical analysis of vegetation was provided by Conrad Pilditch.

**Conflicts of Interest:** The authors declare no conflict of interest.
