Long-term sediment decline causes ongoing shrinkage of the Mekong megadelta, Vietnam.

Since the 1990s the Mekong River delta has suffered a large decline in sediment supply causing coastal erosion, following catchment disturbance through hydropower dam construction and sand extraction. However, our new geological reconstruction of 2500-years of delta shoreline changes show that serious coastal erosion actually started much earlier. Data shows the sandy coast bounding river mouths accreted consistently at a rate of +2 to +4 km2/year. In contrast, we identified a variable accretion rate of the muddy deltaic protrusion at Camau; it was < +1 km2/year before 1400 years ago but increased drastically around 600 years ago, forming the entire Camau Peninsula. This high level of mud supply had sharply declined by the early 20th century after a vast canal network was built on the delta. Since then the Peninsula has been eroding, promoted by the conjunction of mud sequestration in the delta plain driven by expansion of rice cultivation, and hysteresis of long-term muddy sedimentation that left the protrusion exposed to wave erosion. Natural mitigation would require substantial increases in sediment supply well above the pre-1990s levels.


Introduction
This supporting information provides descriptions and interpretations of sediment cores, details of the core sites, and radiocarbon and optically-stimulated luminescence (OSL) dating.

Description and interpretation of sediment cores
We identified a succession of Holocene deltaic sandy and muddy sediments overlying the Pleistocene basement in six sediment cores obtained at sites ST3 and CM2-6 (Figs. 1B and 2, Supplementary Information Table S1). Descriptions and interpretations of these cores, aided by radiocarbon dating (Supplementary Information   Table S2) for chronology, are provided below.

Core ST3
Core ST3 is 24 m long and in contrast to the other five cores consists of well-defined alternations of sand and mud. The basal 2-m interval is distinct from the rest of the succession in terms of consolidation and colour. It exhibits well-defined rhythmic alternations of very fine sand and mud with minor occurrences of burrows and shell fragments. Sand beds are 1-20 mm thick and exhibit parallel and ripple lamination. Mud layers are 1-20 mm thick and massive. Sand-mud ratios range from 1:1 to 2:3. Sporadic burrows are 5-10 mm in diameter and characterized by a thin outline of mud and filling of sand. The colour of this interval is olive brown in sand and greenish to dark greenish grey in mud whereas the rest of the succession is dark to very dark grey except for the upper most 1.5-m interval which is reddish grey. Five radiocarbon ages determined for this interval range from 7.5 to 7.9 ka (except for an older age from mollusk shell considered as reworked material; Supplementary Information Table S2). As the rhythmic alternation suggests tidally-influenced deposition, the basal interval is interpreted as estuarine or deltaic deposits formed in relation to the latest transgression to early regression of the Mekong delta shoreline during the early Holocene. Around a depth of 22 m, the basal interval is overlain by a 20-cm-thick layer of poorly-sorted, muddy very fine sand containing abundant shell fragments and grains of nodules. This poorly-sorted layer is then overlain by a 16-m-thick succession of coarse-silt/sand and mud alternations containing shell fragments and moderate bioturbation. This succession exhibits an upward-coarsening trend in two manners. The grain size of coarser layers intercalated with mud coarsens upwards from coarse silt to lower fine sand. Besides, the sand-mud ratio increases upwards from 2:8 to 9:1. Layers of sand and coarse silt also thicken upwards from 2-5 mm to 1-30 cm. Due to bioturbation, sedimentary structures in sand are generally not well defined, but where identifiable, they are characterized by parallel and ripple lamination. Various burrows are identified and most commonly sandfilled with a thin mud outline or just sand-filled with no outline. The burrow sizes range from 5 to 30 mm in diameter. A similar 3.5 m-thick alternation of sand and mud overlies the upward-coarsening succession at 5.5 m depth but with a slight upward-fining trend from lower fine sand to lower very fine sand. Thirteen radiocarbon ages were determined for the upward-coarsening to fining succession and they are basically consistent with the stratigraphic order. These ages show regressive deposition in relation to the stillstand and slight fall of relative sea level after 5 ka. The consistent upward-coarsening trend up to the depth of 5.5 m represents the progradation of the prodelta and deltafront slope, and the coarsest interval is inferred as the interface between the deltafront platform and slope, where wave energy is attenuated through breaking. The boundary between the poorly-sorted layer and underlying basal interval around 22 m deep was not recovered.
However, this boundary is considered as the ravinement surface as it represents a gap in radiocarbon age around the time interval spanning the transgression to regression and the poor-sorted facies exhibits features of lag deposits. The transgressive surface, defined at the base of the first occurrence of the Holocene marine deposits, should occur below the base of core ST3.

Cores CM2-6
Cores CM2-6 are 10-40 m long (Supplementary Information Table S1) and mostly consist of unconsolidated mud. Cores CM2, 3, and 4 reached the Pleistocene basement which is clearly distinguished from the overlying Holocene succession. While the Holocene succession is unconsolidated and mostly grey to dark grey, the Pleistocene basement is well-consolidated mud and sand coloured greenish grey with reddish yellow to reddish brown patches indicating oxidization. The sediment facies of the Pleistocene succession ranges from massive mud to rhythmic alternations of rippled fine sand and mud suggestive of marine deposition. All cores missed the interval representing the contact between the Pleistocene and Holocene successions. The upper part of the Pleistocene succession at a depth of 17.42 m in core CM4 contains a mollusk shell in burrows dated 4.7-4.9 ka (Supplementary Information Table S2), but the shell is considered to derive from the overlying Holocene deposits due to bioturbation. In core CM3, a 1-m-thick layer of peat overlies the Pleistocene basement. This layer is parallellaminated, organic clay to silt with abundant plant fragments up to 5 cm long. The radiocarbon ages of these plant fragments are consistent, ranging from 9.8-10.0 to 10.2-10.3 ka. Further micropaleontological analysis has not been practiced for constraining the origin of the peat layer. However, according to the relative sea-level curve in this region (Hanebuth et al., 2011), it is likely to be mangrove deposits. The upper boundary of the peat layer is sharp.
In all cores, the rest of the Holocene succession, except for the uppermost 0.5-3 m thick interval, is monotonous, massive mud intercalated with thin lenses of coarse silt and very fine sand. Lenses of coarse silt and very fine sand are commonly a few millimetre thick. Only a few layers are up to 2-3 cm thick and such layers typically show parallel and/or ripple lamination. In contrast to the systematic trend observed in core ST3, it is not possible to discern vertical trends in grain size and thickness in cores CM2-6.
Burrows are ubiquitously identified as patches commonly 2-10 mm in diameter and filled with coarse silt and very fine sand. The succession contains plant fragments and shallow-marine mollusk shells, such as Veremolpa micra, Barbatia virescens, and Moerella jedoensis. The interval 1-3 m deep in core CM3 is a peat layer composed of organic clay to silt with abundant plant fragments. Again, the origin of this peat layer has not been constrained by micropaleontology but is likely from mangroves because of its proximity to the mean sea level. The uppermost interval of all cores is oxidized and contains rootlets. Shell and plant fragment samples from the Holocene succession, except for the basal peat in core CM3, are dated younger than middle Holocene and define a younging trend towards the southwest. These features indicate the regressive deposition of a subaqueous delta in relation to the stillstand and slight fall of relative sea level after the middle Holocene. The boundary of the succession with the basal peat in core CM3 and Pleistocene basement in cores CM2 and CM4 is defined as the transgressive surface.

Radiocarbon dating
Accelerator mass spectrometry (AMS) radiocarbon dating of shells and plant fragments from the sediment cores was practiced by Beta Analytic Inc. (Table S2). The ages obtained were converted into calendar ages by the program CALIB 7.1.0 (Stuiver and Reimer, 1993) using the data set MARINE13.14c with a delta R of -60 ± 28 years for the shell samples and INTCAL13.14c for the plant fragment sample (Reimer et al., 2013).
The delta R was a weighted mean of data at the nearest two points (Southon et al., 2002;Dang et al., 2004). All ages are presented with 2 σ errors with the year 2015 at the datum.

Sample preparation, OSL measurements, and dose-rate determination
Sediments for OSL dating at the auger boreholes were obtained by hammering a lighttight stainless tube 20-30 cm long and 6.5 cm in diameter into sediment that had not been exposed to light. A shorter plastic tube 15 cm long and 5 cm in diameter was then hammered into the stainless tube for transport to the laboratories. Sample preparation and measurements for OSL dating were done at the luminescence laboratories of the University of Sheffield and Geological Survey of Japan. Samples were prepared under controlled red light to avoid affecting the quartz OSL signals. Sediment within 20-25 mm of the ends of the plastic tube was removed and used for measurements of water content and dosimetry. The remaining samples were processed for luminescence measurements.
For sand samples obtained at beach-ridge sites, quartz grains representing a coarse fraction 120-180 µm in diameter were extracted from bulk samples following the method of Bateman and Catt (1996). Mud samples from the muddy plain were processed with hydrochloric acid, hydrogen peroxide, and settling cylinder to extract polymineral fine grains of 4-11 µm diameter. The fine quartz grains from these samples were further purified by processing the polymineral grains with hexafluorosilicic acid. Monolayers of quartz were mounted on 9.8 mm in diameter disks to form large (8 mm in diameter) aliquots, which were then measured with a TL-DA-20 automated Risø TL/OSL reader equipped with blue LEDs for stimulation and a 90 Sr/ 90 Y beta source for laboratory irradiation. Emitted OSL through a Hoya U-340 filter was measured with a photomultiplier.
The single-aliquot regenerative-dose (SAR) protocol was used to determine the equivalent dose (De) using the OSL response to a test dose to monitor and correct for sensitivity changes (Murray and Wintle, 2000). OSL measurements were made at 125 °C.
Preheat plateau test and dose recovery test were carried out on samples Shfd12012 and gsj16191 by changing the preheat temperature from 160 to 260 300 °C in 20 °C increments (Fig. S1). Thus, preheat temperatures of 240 and 220 °C were chosen for the coarse and fine grain samples, respectively. A 160 °C cut-heat for the OSL response to the test dose was used for all samples. To determine De, four regeneration points were measured including 0 Gy and a replicate of the first regeneration point, which was used to check whether the sensitivity correction procedure was performing adequately. Data from aliquots were rejected if recycling ratios were beyond 1.0 ± 0.1. Feldspar contamination was also checked by using the IR ratio test. 20 and 8 replicates per sample were measured for coarse and fine grain samples, respectively ( Fig. S2; Table   S3).
The contributions of both natural radioisotopes and cosmic radiation were considered for determination of the environmental dose rate (Table S3). Concentrations of potassium, uranium, thorium, and rubidium were quantified by inductively coupled plasma mass spectrometry and were converted to dose rate based on data from Adamiec and Aitken (1998) and Marsh et al. (2002). Past changes of moisture content are unknown, so an uncertainty margin of 5% was applied to the measured moisture content values. Cosmic dose rate was estimated based on Prescott and Hutton (1994). The attenuation factors used for beta and alpha rays were based on Mejdahl (1979) and Bell (1980), respectively.
For fine grain samples, we used an a-value of 0.038 ± 0.002 (Rees-Jones, 1995). The final De value was determined by applying the Central Age Model (Galbraith et al., 1999) for individual samples. Statistical outliers were removed using a criterion that removes aliquots with De that falls outside the 25th and 75th percentiles (Fig. S2). De values were then divided by environmental dose rates to obtain OSL ages. All ages are expressed relative to AD 2016 (Table S3) Table S2 Radiocarbon dating results of plant fragments and Mollusc shells in the sediment cores ST3 and CM2-6. Core depth is relative to the ground at the individual core site. 2s calibrated age in ka (thousand years ago) relative to AD2015 is also shown, and those used in Fig. 2