Two sets of field surveys were conducted in 2019 and 2020 to investigate mangrove root structure. The field sites included natural mangrove forests in the Iriomote Island of Okinawa, Japan, and a planted mangrove area in Tarawa, Kiribati.

Iriomote Island, one of the Yaeyama Islands in Okinawa Prefecture, Japan, is a subtropical island located in the Northwest Pacific Ocean, as shown in the upper panel in Supplementary Figure S1. As a part of the Ryukyu Islands Archipelago, Iriomote Island is mountainous (highest altitude: 470 m) with 29 rivers culminating in the coast. The island is 290 km² in area, and the majority of its landmass is covered by natural forests, in which 85% is national forests. Mangrove forests are mainly located in the low-lying areas along the rivers with several species such as Rhizophora stylosa Griff. and Bruguiera gymnorhiza L. (Lam.) targeting one of the dominant species distributed in estuaries and tidal areas, R. stylosa, we conducted surveys on natural mangroves along the Urauchi River (the longest river in Iriomote), as shown in the Supplementary Figure S1. Natural mangroves in an estuary were selected for the measurements. The effect of waves is very limited in this area. Several isolated mangroves were picked for field measurements due to the difficulty of imaging measurements.

The other field site was Tarawa, Kiribati, a tropical island located in the Central Pacific Ocean (1°27′ N, 172°58′ E), as shown in the Supplementary Figure S1. Tarawa is an atoll comprising a long flat reef partially enclosing a shallow lagoon with a wide range of astronomical tides. It is 500 km² in area, and the highest altitude is 3 m. R. stylosa has been planted by the International Society for Mangrove Ecosystems (ISME) since 2005 for multiple purposes, such as environmental recovery, coastal protection, and environmental education. Each year around 7,000–11,000 propagules were planted uniformly with 50 cm as the tree spacing by the close group planting method (Baba, 2011) in the designated afforested patches. The afforestation areas are mainly located west of Bonriki in Tarawa with calm coastal environmental conditions to avoid exposure to severe wind waves and swells. The effect of waves is very limited due to geophysical effects in this area. Therefore, the afforested mangroves inside of the atoll were selected for the measurements. Thus, clear records can be obtained, including the date of afforestation, density, and others in this area. Comparing with natural forests, the afforested mangroves in Tarawa provided an ideal condition to investigate the relationship between mangrove root structure and the associated tree age (Supplementary Figure S2).

In both surveys, the fieldwork included the manual measurements of the representative parameters of mangrove root structure and the use of a 3D laser scanner for detailed root structures. In addition, the 2D projected visualization of mangrove root shapes was obtained by using a digital camera in Iriomote Island. As the 2D and 3D visualization measurements required space, we selected front trees of groups, but the basic tree characteristics (e.g., tree heights, DBH, or age) were measured both front and inside of trees in Tarawa. In this paper, we analyzed the field measurements and the 2D image visualization of mangrove root system structure. At the same time, the 3D scanned data will be presented in the forthcoming analysis along with further field surveys in future work.

Firstly, we measured the characteristic geometry of mangrove structure, R. stylosa, in fields. As shown in Figure 1, the measured parameters included the tree height H and the trunk diameter at breast height (DBH), which refers to the measured diameter at 1.30 m above the ground. We also measured the trunk diameter at the top of the root system D ₁ (equivalent to DBH for a shorter tree), the height of the root system H _root , and the spanning radius of the root system W (i.e., the distance from the tree trunk to the outermost root). Note that the spanning radius was measured in six major orientations whose average was used as characteristic W. The six orientations of spanning radius were combined major two axes plus four major roots. Furthermore, avoiding the difficulty of measurement, the diameter of individual roots was measured at 20 cm above the ground, and the number of prop roots N was recorded. Forty-two trees were picked for field measurements in Iriomote Island and four trees in Tarawa, Kiribati.

In addition to the measurements of the representative parameters of mangrove root structure, we collected the 2D images of mangrove roots using a digital camera (Olympus TG-6, 4,000 × 3,000 pixels) along with a whiteboard as the background (Figure 1). The 2D images were taken in two different directions in two major axes of the root system, and no image correction was applied due to the difficulty of the detail of calibration in the field. Following the previous studies (salt marsh by Lemein et al., 2015, mangrove by Maza et al., 2017), the projected area of the root system A _root can then be estimated by image processing as shown in Supplementary Figure S2. We summarize the procedures for image processing as follows.

1. Binarize the image using the threshold values of the RGB image.

Note that step 2 focuses on the image analysis, excluding the outside area of the root system. Image preprocessing in steps 1 and 2 can reduce the misperception of the analysis. In some cases, sunlight may disturb the color intensity of the image; therefore, the effect was corrected in steps 2 and 3 manually. The counted number of pixels was in the range 10,000–242,000, which is equivalent to approximately 300–3,700 cm². As the number of pixels was sufficient to capture the area of the root system, the accuracy of the estimated projected area was reliable for further discussions with other parameters.

We first examined the measured tree height and the main geometric parameters of the root system. Major three axes were analyzed by the 2D imaging following Methodology. In Figure 2, a proportional relationship can be seen between the tree height H and the spanning radius of the root system W. Asymmetric root system can also be observed for shorter trees (approximately <180 cm). These morphological characteristics of mangrove trees and root systems are discussed in this section. As the spanning radius of the root system varied in different orientations, the averaged value was applied hereafter.

Figure 3A shows the relationship between the tree height H and the spanning radius W by Iriomote Island and Tarawa with two empirical fitting formulas presented by blue and red solid lines, respectively. Note that zero intercepts were assumed when defining the empirical fitting formula. Obviously, these two parameters are highly correlated, as presented in Figure 2. Although the data in Tarawa is fewer than Iriomote Island, two different data in different locations show the quite similar relation for H and W. Next, the relationship between the tree height H and the trunk diameter at breast height DBH for Iriomote Island data with the empirical fitting formula is shown in Figure 3B. According to the measurements, the tree height increases linearly with smaller DBH (<25 mm) and tends to be convergent around 300 cm for larger DBH (>30 mm) within the measured DBH range (<50 mm). Note that the comparison with the results in Ohira et al., 2013 for Rhizophora apiculata Blume and Rhizophora mucronata Lam. with this dataset is quite similar but slightly higher tree height by the current parameterization for R. stylosa.

Secondly, we discussed some of the representative parameters of the root system. Supplementary Figure S4 shows the proportional relationship between the height of the root system H _root and the number of prop roots N, which can be expected as a part of the natural growing process. Note that the height of the root system was estimated by analyzing the 2D images taken from different orientations (Methodology), and an averaged value (with an asterisk) is presented here. The results reported in Ohira et al., 2013 were also included in the same figure for comparison, although their target mangrove species are R. apiculata and R. mucronata.

In addition to the relationships among distinguishing factors of mangrove root structure, another objective of this study was to understand the intertwined connections between the aforementioned geometric parameters and the projected area of the root system, which is critical to establish the proper parameterization of mangrove effects as shown in Eq. 1. Therefore, we here present the projected area of the root system A r o o t ∗ and its relationships with two representative parameters of mangrove root structure—DBH, and H r o o t ∗ . In Figure 4A, the projected area A r o o t ∗ increases with DBH, in which DBH approximately ranges from 8 to 52 mm, monotonically. The projected area A r o o t ∗ against the height of the root system H r o o t ∗ can be found in Figure 4B, showing a quadratic proportional relationship. Both the relation of DBH and H r o o t ∗ to A r o o t ∗ shows quadric increases as their increase. It indicates the nonlinear increase of wave damping by the root system as the mangrove becomes larger. Furthermore, Figure 5 shows the normalized A r o o t ∗ in terms of the normalized vertical distance z from the bottom by H r o o t ∗ . Both the ensemble average and its standard deviation are presented. The normalized frontal area quadratically increases from the bottom, and it gradually approaches the maximum near the top of the root system. As observed in fields, the projected area of mangrove roots shows nonlinear profiles (unlike other coastal trees with relatively simple geometry), which need to be properly parameterized, especially under low water-level conditions.

The current analysis obtained the empirical relationships among the representative parameters of mangrove root structure and the root system. Although solely using the relationship based on DBH in numerical modeling may yield uncertainties by ignoring the contributions from other factors, the above results relate other characteristics of mangrove root structure (e.g., height of the root system, the number of prop roots and the frontal area of the root system) which shall compensate the parameterization in numerical modeling.

As presented in the previous section, the bulk geometric characteristics of mangroves and the root system can be parameterized as a function of tree height H, DBH, and height of prop roots H r o o t . On the other hand, the information on these parameters and their variation in time is critical to assess mangrove effects on wave damping, especially when conducting afforestation or reforestation. The potential impact of growth rate on mangrove root structure should also be included in the development of numerical models for longer time-scale estimation (e.g., in 10 years or later).

In Figure 6A, we first present the relationships of tree age with the tree height (circles) and the height of the prop roots (triangles) by Kiribati data. The regression curves (dashed lines) obtained by the least-square fitting method are included in the same plot. A higher growth rate of the tree height was observed in comparison with that of the root system. Recalling the quasi-linear relationship between H and W in Figure 3A, the increasing rate of the spanning radius of the root system (as well as the number of prop roots) can be expected to be greater compared to the growth rate of the height of mangrove roots. It should also be noted that the growth or height of the root system is not only determined by age but also the other environmental conditions. Therefore, the shown relation in Figure 6 is neither directly related to Iriomote Island data or general. The field variation and the different site-to-site environmental conditions should be considered when discussing the proper parameterization quantitatively. However, the summary of the combined field data can give us the first approximation of mangrove shape parameterization for hydrodynamic modeling.

In Figure 6B, the diameter D ₁ is plotted versus the tree age. Note again that D ₁ denotes the trunk diameter right above the root system. A clear linear relationship can be observed in Figure 6B, and the regression curve is also provided. The diameter D ₁ approximately ranges from 15 mm (3-year-old tree) to 25 mm (11-year-old tree). The empirical relationships in Figures 6A,B provide a valuable reference to estimate the variation of the representative parameters of mangrove root structure in time.