On the ecogeomorphological feedbacks that control tidal channel network evolution in a sandy mangrove setting

An ecomorphodynamic model was developed to study how Avicennia marina mangroves influence channel network evolution in sandy tidal embayments. The model accounts for the effects of mangrove trees on tidal flow patterns and sediment dynamics. Mangrove growth is in turn controlled by hydrodynamic conditions. The presence of mangroves was found to enhance the initiation and branching of tidal channels, partly because the extra flow resistance in mangrove forests favours flow concentration, and thus sediment erosion in between vegetated areas. The enhanced branching of channels is also the result of a vegetation-induced increase in erosion threshold. On the other hand, this reduction in bed erodibility, together with the soil expansion driven by organic matter production, reduces the landward expansion of channels. The ongoing accretion in mangrove forests ultimately drives a reduction in tidal prism and an overall retreat of the channel network. During sea-level rise, mangroves can potentially enhance the ability of the soil surface to maintain an elevation within the upper portion of the intertidal zone, while hindering both the branching and headward erosion of the landward expanding channels. The modelling results presented here indicate the critical control exerted by ecogeomorphological interactions in driving landscape evolution.


Specification of inundation and competition stress factors
When developing the correction factors for mangrove growth resulting from inundation (I) and competition (C) stress, it is of specific interest when these factors reach a value of 0.5, as this determines when mangrove mortality occurs. I is a function of the hydroperiod and we relate the two as: where P represents the relative hydroperiod (T (inundated) /T (tide) ) and a, b, and c are constants which have been set to 4, -8, and 0.5, respectively. Equation (1.1) suggests that there is a maximum growth rate for a specific hydroperiod. Growth rates are reduced when the mangroves are inundated for either longer or shorter (figure S1a). The values of a, b , and c were chosen such that I = 0.5 when the mangroves are inundated for half of the time (P = 0. 5) or when the mangroves are not inundated at all (P = 0). Mangrove trees stop growing completely when they are inundated for longer periods of time (P > 0.6). C is determined by the total biomass B and we apply a sigmoid function to relate the two (figure S1b): where d is another constant and is set to -0.00005 and B 0.5 is the value of B for which C = 0.5.
In order to compute B, we consider the total number of mangrove trees per grid cell and the weight of each single tree W tree , which is given by the summation of the above-ground W tree,a and below-ground W tree,b tree weight:

Implementation of the effects of mangroves on physical processes
Aquatic plants are well-known for offering additional resistance to the flow [3]. Mazda et al. [4,5] performed a theoretical analysis based on the momentum equation to show that the drag force by mangroves is strongly dependent on the total projected area of obstacles A and the total volume of obstacles V M in a certain control volume V. They related the drag coefficient to a characteristic vegetation length scale L which was defined as: The height of control volume V equals the local water depth and L can thus vary during a tidal cycle [4,5]. In addition, L contains information about the spacing between the trunks and roots of the mangrove trees and L decreases (decreasing spacing) with increasing V M and A.
The drag coefficient C D is thus inversely correlated with L and the effect is here described by: where C D,no is the drag coefficient when no mangroves are present and this is set to a standard value of 0.005. e is a dimensional constant and set to 5 m to obtain realistic values for C D .
The application of equation (2.2) requires a description of the number of pneumatophores per tree N pneu . Pneumatophores are the vertical aerial breathing roots that the trees use to adapt to tidal flooding and the low oxygen supply in sediments. They can grow to a few tens of centimetres high [6] and thus increase the overall flow resistance. A single Avicennia marina tree can have more than 10000 of these vertical roots [7]. We developed a sigmoid function which relates N pneu and the stem diameter such that the number of pneumatophores is 10000 for a tree with a stem diameter equal to D max :  [4,5]. The effect of mangroves on drag can be incorporated in the numerical model as a bottom friction [8,9]. The drag coefficient values computed following equation (2.2) were thus used as input for the bottom friction formulation within the hydrodynamic model and, as such, the mangroves directly affected hydrodynamic conditions. Sediment transport rates are calculated in the model with the Engelund and Hansen [10] formula which is traditionally written as: where θ is the Shields parameter which is given by: Equations (2.5) and (2.6) allow for an erosion threshold which is dependent on the belowground biomass. No extensive data sets are available to parameterize the effects of Avicennia marina on sediment erodibility. We therefore adopted and modified a formulation based on the work by Mariotti and Fagherazzi [12], who linearly correlated the increase in erosion threshold with biomass in their model of salt marsh dynamics: where θ cr,no is the critical Shields parameter when no mangroves are present and is set to 0.06 such that the sediment transport model reduces to equation (2.4) when mangroves are not present. B b is the below-ground biomass and B b,mature is the below-ground biomass of 125 mature (D=D max ) mangroves. K cr is a constant and we use a value of 0.1 so that θ cr is 10% larger in a mature mangrove forest. Following equations (2.5), (2.6), and (2.7), a 10%increase (θ cr =0.066) implies that no sediment transport occurs for a flow velocity below 0.31 m/s. Because of the self-thinning process in the mangrove forest, it is possible that during the development of the forest, although the below-ground tree weight per tree is lower, the large number of individuals causes B b to be higher than B b,mature . However, in the model we restrict the ratio between B b and B b,mature in equation (2.8) so that it cannot exceed 1.
The roots of mangrove trees do not only increase the sediment's resistance to erosion by the tidal flow, they also decrease the magnitude of slope-driven sediment transport fluxes and allow steeper slopes to develop in the morphology. Modelling efforts, which have previously explored the effects of a reduction in gravitationally driven sediment transport by vegetation [13,14]), applied a reduction by approximately two orders of magnitude in the case of fully developed vegetation. Similar to Kirwan and Murray [13], the slope-driven sediment transport S slope is proportional to the bed slope: where b is the slope towards the neighbouring grid cell. Slope-driven sediment transport only occurs when b exceeds 0.01. This threshold is used so that channel initiation is not hindered and to avoid indefinite channel widening. The ratio between B b and B b,mature is again not allowed to exceed 1. We here took a conservative approach and applied a maximum reduction of S slope by one order of magnitude and the values of the dimensional constants α (1.1574  10 -5 m 2 /s) and β (1.0417  10 -5 m 2 /s) were chosen accordingly. If mangroves are not present, equation (2.9) reduces to the transport formulation used in van Maanen et al. [15]. Parameterizing the slope-driven sediment transport term is not straightforward and although a similar type of formulation was previously used for salt marsh channels [13], the approach was initially developed for fluvial channels [14]. Further research is clearly needed to test and develop improved representations of gravitationally driven sediment fluxes.
The production of organic material by the mangroves raises the soil surface by a few millimetres per year [16]. Numerical models to study the dynamics of salt marsh systems usually apply a linear relationship between the production of organic matter and biomass [12,[17][18][19]. The main component of organic deposits in mangrove forests is refractory roots with leaf litter playing a secondary role [20]. We therefore related the elevation change due to organic production ∆Z org to the below-ground biomass: where K org is a characteristic accumulation rate. Little information exists on root volumetric input and detailed measurements of accumulation rates for Avicennia marina are unfortunately not available. Field measurements collected for other species suggest that a wide range of accumulation rates is possible [16]. We decided to set K org to a conservative 1 mm/year.

Use of aerial photographs to analyse the effects of mangroves
Although a different type of system from the one simulated in the present study, aerial photos from the Firth of Thames estuary (North Island, New Zealand) show how the spreading of mangroves influenced channel geometry. The Firth of Thames is unusual in that mangrove habitat has rapidly expanded over the last 50 years as a result of catchment deforestation and increased sediment delivery to the estuary [21]. Although it remains difficult to elucidate vegetation effects from aerial photos (and that is why controlled numerical modelling experiment are valuable), figure S2 shows that the geometry of one of the rivers that flows into the estuary has undergone several changes while mangrove growth expanded, including narrowing (and presumably deepening) of the channel and steepening of the channel banks. Figure S2. Mangrove expansion and related changes in channel geometry of one of the rivers flowing into the Firth of Thames estuary, North Island, New Zealand.