Natural flood risk management in the tropics: Prospects in the biodiverse archipelagic nation of the Philippines 

The concavity index, $\theta$, describes how quickly river channel gradient declines downstream. It is used in calculations of normalized channel steepness index, $k_{sn}$, a metric for comparing the relative steepness of channels with different drainage area. It is also used in calculating a transformed longitudinal coordinate, $\chi$, which has been employed to search for migrating drainage divides. Here we quantify the variability in $\theta$ across multiple landscapes distributed across the globe. We describe the degree to which both the spatial distribution and magnitude of $k_{sn}$ and $\chi$ can be distorted if $\theta$ is assumed, not constrained. Differences between constrained and assumed $\theta$ of 0.1 or less are unlikely to affect the spatial distribution and relative magnitude of $k_{sn}$ values, but larger differences can change the spatial distribution of $k_{sn}$ and in extreme cases invert differences in relative steepness: relatively steep areas can appear relatively gentle areas as quantified by $k_{sn}$. These inversions are function of the range of drainage area in the considered watersheds. We also demonstrate that the $\chi$ coordinate, and therefore the detection of migrating drainage divides, is sensitive to varying values of $\theta$. The median of most likely $\theta$ across a wide range of mountainous and upland environments is 0.425, with first and third quartile values of 0.225 and 0.575. This wide range of variability suggests workers should not assume any value for $\theta$, but should instead calculate a representative $\theta$ for the landscape of interest, and exclude basins for which this value is a poor fit.

Since 1973 micro-erosion meters (MEM) have been used at Kaikōura Peninsula to determine lowering rates on inter-tidal shore platforms. Rates measured over two, two year periods (1973-1975 and 1994-1996) and at decadal scales (20-30 years) demonstrate that platform surface lowering is on average 1.1 mm/yr. The 14 November 2016 Kaikōura magnitude 7.8 (Mw) earthquake caused an instantaneous uplift of 0.8-1.0 m of the peninsula. The uplift offers the rare opportunity to examine how such an event alters processes and rates of erosion on these shore platforms, since these are now partially marine terraces as the inner margins of some platforms are now above high tidal levels (but perhaps not storm surge). Since the earthquake, 42 MEM sites have been measured seven times at 3 monthly intervals. Most recently in September 2018. MEM sites show widely varying responses to the uplift. Erosion rates are at some MEM sites three times the previous annual rate while other sites show significant amounts of rock swelling (3-4 mm in 6 months), or aggradation as weathered rock fragments are no longer removed by wave action. The coseismic uplift has fundamentally changed the process regime operating on these platforms. Zones of maximum wetting and drying have migrated seaward causing previously slow eroding (< 1 mm/yr) MEM sites to accelerate to twice the pre-earthquake rates. Erosion rates demonstrate rapid adjustment of the platform surface to this disturbance and illustrate how uplifted marine terraces can be rapidly eroded despite being above sea level. The preservation of the new marine terrace is probably dependent on further uplift within the next 300-400 years, otherwise erosion by lowering and backwear will likely remove the new surface. This scenario has significant implications for marine terrace preservation and the recording of coseismic events in the landscape.