Reconstructing sediment pathways in fluvial and deltaic systems beyond instrumental records is challenging due to a lack of suitable methods. Here we explore the potential of luminescence methods for such purposes, focusing on bleaching of the optically stimulated luminescence (OSL) signal of quartz sediments in a large fluviodeltaic system across time and space. We approach this by comparing residual doses of sand and silt from the modern Mississippi River channel with estimated residual doses of sand isolated from Late Holocene Mississippi Delta mouth bar and overbank deposits. Further insight is obtained from a comparison of burial ages of paired quartz sand and silt of Mississippi Delta overbank deposits. In contrast to some previous investigations, we find that the bleaching of the OSL signal is at least as likely for finer sediment as for coarser sediment of the meandering Mississippi River and its delta. We attribute this to the differences in light exposure related to transport mode (bedload vs. suspended load). In addition, we find an unexpected spatiotemporal pattern in OSL bleaching of mouth bar sand deposits. We suggest this may be caused by changes in upstream pathways of the meandering channel belt(s) within the alluvial valley or by distributary channel and coastal dynamics within the delta. Our study demonstrates that the degree of OSL signal bleaching of sand in a large delta can be highly time- and/or space-dependent. Silt is shown to be generally sufficiently bleached in both the modern Mississippi River and associated paleo-deposits regardless of age, and silt may therefore provide a viable option for obtaining OSL chronologies in megadeltas. Our work contributes to initiatives to use luminescence signals to fingerprint sediment pathways within river channel networks and their deltas and also helps inform luminescence dating approaches in fluviodeltaic environments.
Relatively few tools presently exist to reconstruct sediment pathways within river and delta channel networks beyond instrumental (less than centennial or decadal) timescales, despite the high value of such information to human management of waterways. For example, improved knowledge of waterborne sediment pathways is a key component to delta restoration initiatives, such as river diversions aiming to mitigate land loss in deltas through delivery of sediment to the delta plain (e.g., CPRA, 2017). These engineered outlets will siphon sediment from yet-to-be-determined depths and positions within the river channel, and so the availability and grain size of the utilized sediment will depend on its transport mode within the river (e.g., Esposito et al., 2017) as well as the location and geometry of the engineered feeder channel (e.g., Gaweesh and Meselhe, 2016). Similarly, the sustainability of such restoration strategies may hinge on the recharge timescales of riverbed sandbars, a poorly constrained parameter.
The luminescence signals of sediment grains provide a unique and underexplored archive for reconstructing channel network dynamics and evolution, as they contain information regarding the transport histories of grains. Luminescence dating (Huntley et al., 1985; Hütt et al., 1988) and its subsequent methodological advances (e.g., Cunningham and Wallinga, 2010; Galbraith et al., 1999; Murray and Wintle, 2000, 2003; Cunningham and Wallinga, 2012) have enabled new chronologies of fluvial and deltaic systems, obtained from direct measurements of the burial time of clastic sediment. Yet, relatively few studies have applied this tool to trace earth surface processes (see Gray et al., 2017; Reimann et al., 2015; Sawakuchi et al., 2018; Liu et al., 2009; Keizars et al., 2008; Forman and Ennis, 1991). Of note, Liu et al. (2009) used feldspar thermoluminescence (TL) signals to study sand transport pathways in a fluvial and coastal system in Japan, while Reimann et al. (2015) used bleaching of multiple luminescence signals to track the dispersion of sand grains along the Dutch coast following human emplacement for coastal engineering. Gray et al. (2017) designed a model to estimate fluvial sediment flux based on upstream-to-downstream bleaching of sediments observed in the Loire and Mojave rivers. These studies all focused on modern deposits rather than utilizing the archive of (pre)historic sediments.
Here, we explore luminescence signal resetting (“bleaching”) as a means of reconstructing the fluvial pathways of sediments in Late Holocene deposits. Bleaching of the luminescence signal by sunlight exposure of at least some of the grains within a sample upon burial is a key component of luminescence dating; in other words, the luminescence clock of at least some grains must be zeroed shortly before or at the time of the event of interest (e.g., Wallinga, 2002). In the absence of complete resetting, sediment grains retain a residual dose acquired during previous burial. Populations of sediment grains (e.g., sediment samples) may be completely (well) bleached and contain only zeroed grains, or they may be incompletely bleached and contain at least some grains with residual doses (Duller, 2008). Here, we further classify incompletely bleached sediment populations as heterogeneously (containing both zeroed grains and grains with residual doses) or poorly bleached (containing few to no zeroed grains).
Assessing luminescence signal bleaching is important for dating applications because incomplete bleaching may lead to overestimation of the time of the most recent burial event. Incomplete bleaching is especially a concern for dating fluvial sediment deposited within the most recent millennium because some grains may receive little light exposure during river transport, and even small residual doses can produce highly inaccurate ages on young deposits (Wallinga, 2002). A number of studies have investigated the degree of bleaching of river deposits and sediment entrained within modern river channels and its relationship to grain size and geography, primarily for the purpose of improving dating fidelity. This has been approached through tests of modern sediment or those of independently constrained depositional ages. These studies have returned wide and varied results. Some have found that coarse sand is better bleached than fine sand (e.g., Olley et al., 1998, for the Murrumbidgee River, Australia; Truelsen and Wallinga, 2003, for the Rhine Meuse Delta, the Netherlands). Well-bleached silt has been identified in suspension in the Yangtze River (Sugisaki et al., 2015) and its Holocene deposits (Nian et al., 2018; Gao et al., 2018) as well as in recent (decades- to centuries-old) deposits of the Ganges–Brahmaputra Delta (Chamberlain et al., 2017). Yet, incomplete bleaching of silt has been shown for other fluvial systems such as fluvial terrace deposits of northwest China (Thompson et al., 2018) and flood deposits of the Elbe River and a tributary in Germany (Fuchs et al., 2005).
The mechanisms that dictate the degree of bleaching of fluviodeltaic sediments are also not known to be absolute or universal. For example, bleaching of sand may increase on average with transport distance due to sunlight exposure during temporary storage on bar surfaces (Stokes et al., 2001) or may decrease downstream due to the addition of poorly bleached grains by tributaries or local bank erosion (McGuire and Rhodes, 2015). Sediment entrained within a river channel may be less well bleached if temporary storage on the riverbanks is limited because turbid water reduces the intensity of light exposure and restricts the light spectrum (Berger et al., 1990). Yet, in-channel transport offers an opportunity for sunlight exposure of sediment transported near the water surface, especially finer grains that are more evenly distributed in the water column (Fuller et al., 1998), or those in turbulent systems (Gemmell, 1988). Bleaching of entrained sediments may also occur during subaerial exposure of river bar surfaces under conditions of low water discharge (Cunningham et al., 2015; Gray and Mahan, 2015). Furthermore, sediment grains in transit may experience different bleaching than those preserved in the stratigraphic record (Jain et al., 2004) because in-transit grains have not yet reached their final destination and therefore have not necessarily undergone the full range of bleaching opportunities.
Our research aims to clarify the degree and mechanisms of luminescence signal bleaching in fluviodeltaic sediments so that this tool may be applied to sedimentary archives to reconstruct sediment transport histories. We approach this through an investigation of residual doses of quartz sediments of the contemporary Mississippi River and associated Late Holocene deltaic deposits (Fig. 1). Using recently proposed and tested methods (Chamberlain et al., 2018b) to analyze archival data, we compare the residual quartz optically stimulated luminescence (OSL) doses of sand and silt sampled within the modern Mississippi River channel (Muñoz et al., 2018; Chamberlain et al., 2018b; Chamberlain, 2017) to those estimated from sand of multi-century to millennium-aged Mississippi Delta mouth bar (Chamberlain et al., 2018a) and overbank (Shen et al., 2015) deposits. Further insight into OSL bleaching is obtained by reanalyzing the burial ages of paired quartz sand and silt of Mississippi Delta overbank deposits (Shen et al., 2015). All combined, these data allow us to test whether OSL signal bleaching varies across time, space, grain size, and depositional environment, even within a single fluviodeltaic system.
The Mississippi Delta and catchment
The Mississippi River is among the largest rivers in the world in terms of
catchment size, sediment, and water discharge. Its catchment includes about
The hydrograph of the Mississippi River is generally highest in the spring
due to snowmelt and increased precipitation in the catchment, and it has
multiple spring peaks with an average discharge of 25 000 m
In addition to being a major river with significant variance driven by natural sources, the Mississippi is presently one of the most highly engineered river systems in the world (Kesel, 2003; Allison et al., 2012). Flow within the contemporary Lower Mississippi River is generally contained by human-made levees, which limit the degree of interaction of the channel with its floodplain and decrease the cannibalization of banks by restricting river migration (Kesel, 2003). Throughout the Holocene and prior to modification, the Mississippi River meandered freely within a series of six channel belts of unknown absolute ages (Saucier, 1994). The construction of dams as well as flood and navigation control structures in the catchment has reduced the suspended sediment load reaching the delta by reported values of 50 %–70 % (Blum and Roberts, 2009; Kesel, 2003), although the effects of these structures on sand transport to and within the deltaic reach have been debated (Nittrouer and Viparelli, 2014; Blum and Roberts, 2014). Similar changes in hydrology and sediment transport due to engineering have been documented in other fluviodeltaic systems (e.g., Hobo, 2015; Erkens, 2009). An investigation into bleaching that considers the residual doses of sediments of both pre-anthropogenic and present-day conditions is therefore useful because the hydrology and related luminescence bleaching opportunities of grains in the Mississippi River and other major channels worldwide may have been quite different prior to human modification of rivers.
The Holocene Mississippi Delta first emerged around 7 ka, as sediment
delivery to the basin outpaced regional sea-level rise
(Törnqvist et al., 2004), and is composed of a series
of amalgamated sediment lobes (subdeltas) fed by discrete distributary
networks (Fisk, 1944). This study mainly investigates deposits of the
presently 10 000 km
Previous research applying OSL dating to Lafourche subdelta deposits mainly
relied on the measurement of small-diameter aliquots (that is, numerous
subsamples for each sample, each containing
This study uses quartz OSL data compiled from previous investigations of contemporary sediments of the Mississippi River (Muñoz et al., 2018; Chamberlain et al., 2018b; Chamberlain, 2017) and associated prehistoric deltaic deposits (Chamberlain et al., 2018a; Shen et al., 2015) (Fig. 1, Table S1).
Modern Mississippi River bedload (Chamberlain et al., 2018b) and
suspended load (Chamberlain, 2017; Muñoz et al., 2018)
sediments were sampled at Bonnet Carre Upstream 2 (BCU2), a site 221 river
kilometers above the Mississippi River mouth at Head of Passes (Fig. 1).
This site corresponds to the AboveBC2 site in Allison et
al. (2013). Sampling took place in the Mississippi River channel center
during high-flow conditions of 18 320 m
To investigate bleaching of older sediments, we revisited samples of Late
Holocene Mississippi Delta sediments ranging in age from 1.6 to 0.6 ka,
previously collected and measured by Shen et al. (2015)
(overbank deposits,
Samples were prepared following standard procedures, which are described in
the primary publications, and were generally consistent across datasets.
Measurements of small-diameter (
Estimating residual doses of in-transit modern sediments is fairly
straightforward because these should yield a zero
In the absence of independent age control for individual samples (e.g.,
historical records of deposition), the estimation of the residual dose of
paleo-deposits is not straightforward. Here, we estimated the residual doses
of Late Holocene deposits as the difference in
Radial plots of four mouth bar sand samples provide an example of
our approach to assessing the degree of bleaching of Late Holocene deposits.
Our assessment is based on the residual dose, given in parentheses, obtained
from the difference in equivalent doses (
Age modeling for the paleo-deposit sand samples was revisited by
Chamberlain et al. (2018b) using the bootstrapped (Cunningham and Wallinga, 2012) Minimum Age Model (Galbraith
et al., 1999) (bootMAM). This study also employed a novel approach to assign
the input and uncertainty on the overdispersion (
The doses of silt isolated from paleo-deposits were determined as a mean and
standard error, and we also report central doses obtained with the CAM
(Table S2), which were not used for analysis. The mean has been shown to
yield identical doses as the CAM for silt deposits greater than a few
hundred years in depositional age (Chamberlain et al.,
2017), consistent with our findings here (Table S2). To test bleaching of
Late Holocene silt, we compare the silt ages obtained from the mean to
bootMAM ages of sand isolated from the same sample. The approach is reasonable because (1) within-aliquot averaging disqualifies
the use of a minimum age model, and thus
internal comparison of
Remnant doses preserved in grains upon burial have little direct
relationship with the dose rate of the matrix from which the grains are
ultimately isolated for luminescence dating, although the dose rate of this
matrix is often used to determine the residual age. The bulk sediment
characteristics and geological context (e.g., radionuclide activity
concentrations, cosmogenic exposure, water content) under which the residual
doses were acquired are generally unknown. For this reason, we prefer to use
residual dose rather than residual age to describe the bleaching of
sediments if possible. Hence, we use residual dose for all sand extracts
(modern and paleo-deposit) and for modern river silt extracts (see Sect. 3.2). Approximations of residual age are also discussed for the sand
extracts and modern river silt extracts, as it relates to potential
inaccuracies in burial age estimates if incomplete bleaching is not
adequately addressed. These are informed by average (
Ages calculated for the comparison of sand and silt fractions isolated from the same sample used the dose rates particular to those samples that are presented in Shen et al. (2015). These ages were calculated by dividing the paleodose of each sample by its dose rate, taking both random and systematic uncertainties into account, and propagating uncertainties in quadrature. All dose rates from Shen et al. (2015) were updated here to use the radionuclide conversion factors of Guérin et al. (2011) (Supplement, Table S1). Other dose rate details can be found in the original publications.
Residual doses of all samples are provided in the Supplement, Table S1. Modern river sediments show a trend of increasing residual dose with
both grain size and sampling depth below the water surface (Fig. 3). We
found that residual doses of modern river silt, moving in suspension within
the channel, are very low regardless of water depth (note the logarithmic
scale of Fig. 3). These ranged from
Residual doses of quartz silt and sand from sediments in transit in the modern Mississippi River, with sample depth in the river channel.
Of the two coarse silt (45–75
Residual doses of modern river fine silt appeared to be slightly greater
with depth in the channel (Fig. 3). This may suggest some stratification of
the water column. Alternatively, and more likely, the apparent trend may
reflect different grain size distributions within the analyzed fractions.
Although the same fraction (4–20
By contrast, both grain size fractions of modern river bedload sand (BCU2
I-6) appeared to be heterogeneously bleached. The residual dose of the
125–180
As there is uncertainty on the
Residual doses calculated as
Among all samples, we observed a trend of increasing residual dose with
increasing median grain size (Fig. 5), suggesting that coarser sand may be
the least likely grain size to be completely bleached in this system. Still,
each sand grain size fraction also contains some well-bleached samples,
indicating that sand grains of all investigated sizes could be bleached
prior to preservation. As discussed above, the 180–250
Mean (boxes) and individual (circles) residual doses by median
grain size (see legend) for silt and sand samples of all depositional
environments. Data are not shown for the 180–250
Surprisingly, the bleaching of mouth bar sand showed a strong temporal trend
(Fig. 6a). All mouth bar sand samples (
Bleaching of sands isolated from mouth bar and overbank deposits
with
As the Lafourche subdelta expanded radially (Chamberlain et al.,
2018a), the temporal trend in bleaching of mouth bar deposits is also
reflected spatially (Fig. 6b). Mouth bar deposits in the upstream reaches
(above
Good agreement was found between the majority (
Comparison of mean ages of silt fractions with ages obtained using
the
By coincidence, the samples selected by Shen et al. (2015) for the paired sand–silt analysis featured sand that we mainly classified as well bleached, with little difference between sand ages obtained with the CAM and the bootMAM (Supplement, Fig. S6). This manifests in similar ages obtained with the mean dose of the silt fraction and the CAM dose of the sand fraction (Fig. 7b). It is possible that greater differences between bleaching of sand and silt could be identified if this test was performed on sediment pairs extracted from deposits with heterogeneously bleached sand.
It is little wonder that universal trends in bleaching of fluviodeltaic sediments have not yet been identified, considering the complex and numerous pathways river sediments may take prior to deltaic deposition and the natural variability among river systems in general. This study, which focused on one large meandering river and its deltaic deposits across time, identified lower average quartz OSL residual doses for finer sand grains than for coarser sand grains. This trend was observed both for in-transit sediment within the river and for sediments preserved within deltaic deposits (Figs. 3 and 5). Our findings with regard to grain-size-dependent sand bleaching are different from those of studies conducted in other systems (Truelsen and Wallinga, 2003; Olley et al., 1998), which featured smaller primary channels and included more samples of coarser grain sizes than investigated here.
We found that fine silt, moving in suspension within the modern river channel, was more completely bleached than sand moving as bedload (Fig. 3) and that bleaching of silt was also generally sufficient in river sediments deposited prior to human engineering of the system (Fig. 7). This is consistent with recent studies of other contemporary large river systems within their deltaic reaches (Sugisaki et al., 2015; Chamberlain et al., 2017), yet different from studies of smaller and/or source-proximal rivers and their deposits (Fuchs et al., 2005; Thompson et al., 2018). As many large rivers are well known to be turbid (e.g., the “Muddy” Mississippi; Morris, 2012; Gramling, 2012; Rutkoff and Scott, 2005), it is possible that turbulence within large and lengthy channels offers sufficient opportunities for bleaching of the finest material moving in suspension via the constant upwelling of the sediment-laden river water.
Bleaching of mouth bar sand (75–125 and 125–180
Geographic distribution of sands and their minimum residual doses, defined as the residual dose minus its uncertainty.
We offer a few plausible explanations for the spatiotemporal trend in
bleaching of mouth bar sand within the Lafourche subdelta (Figs. 6 and 8).
The primary alluvial channel is known to have avulsed a number of times
throughout the Late Holocene (Saucier, 1994; Chamberlain et al.,
2018a) and to have migrated via meandering within its channel belts, thereby
occupying different pathways within the Lower Mississippi Valley (well
upstream of the delta). The timing of channel-belt avulsions and meander
pathways is not well known. It is possible that a relatively landward
avulsion (450–700 linear kilometers inland; see Chamberlain et al.,
2018a) or divergence in a meandering pathway
of the river within one channel
belt circa 1.2–1.1 ka may have positioned the river in such a way that it
mobilized younger deposits, for example by reworking Late Holocene
channel-belt deposits rather than eroding Pleistocene terrace deposits.
Recently bleached sediments would require less light exposure during transit
in the river system to become well bleached upon arrival and deposition in
the delta. Alternatively, the abrupt change in bleaching of mouth bar sand may be
linked to hydrologic changes within the delta itself, associated with the
activation of the Modern (Balize) subdelta circa 1.4–1.0 ka (Hijma et
al., 2017). For example, after 1.2–1.1 ka much of the bedload may have
been rerouted toward the Modern (Balize) subdelta, causing suspended-load
transport during high-flow events to be the more dominant mode of
sand delivery to the lower reaches of the Lafourche subdelta. Under
this scenario, the overbank deposits could be expected to be better
bleached because these are sourced to suspended material (Esposito et
al., 2017). Additionally, decreased discharge in Lafourche distributaries (due to a
partial avulsion to the modern route) or enhanced exposure as Lafourche
channel tips prograded seaward and outside of the shelter of the
pre-Lafourche bay may have allowed marine processes to gain importance,
potentially altering turbulence, turbidity, salinity, and/or suspension
times of sediment at the mouths of Lafourche distributaries. Yet, the
residual doses for overbank deposits also show a change in degree of
bleaching around 1.1 ka. Although this trend is less clear compared to the
mouth bar deposits, it suggests that sediment reworking at the river mouth
is not the only explanation.
It is also plausible that these drivers operated in tandem; an avulsion of
the alluvial channel may have driven delta-lobe switching circa 1.2–1.1 ka and subsequent mobilization of younger sand upstream plus hydrologic
changes at the Lafourche channel mouths that supported more complete OSL
signal bleaching. We do not have sufficient data at present to test these
hypotheses. Bleaching of mouth bar sand was not found to correlate with depth
within the deposit (Fig. 9a), suggesting that improved bleaching was
related to neither reworking of mouth bar surfaces nor bioturbation, which could be
expected to produce greater bleaching for shallower deposits.
Bleaching of mouth bar
Bleaching of overbank deposits was also not found to be improved at shallower depths (Fig. 9b) or with proximity to the trunk channel (Supplement, Figs. S3 and S4). Other possible trends in bleaching of overbank sand merit further testing. The degree of bleaching of overbank sand may be linked to opportunities for bleaching during or immediately after deposition (e.g., Cunningham et al., 2011), or even to the time of year (and therefore water velocity and turbulence within the primary channel; e.g., Allison et al., 2014) that deposits formed.
The discussions above highlight the limitations of our study. Although this is the largest dataset used to examine bleaching of fluviodeltaic sediment to our knowledge, a number of questions remain that are unanswerable with the present data. For example, we observed highly heterogeneous bleaching of the coarsest grain size of modern river bedload sand. Yet, it is unclear whether this would be the case for similar fractions sampled from different locations in the river or at different times of the year. In addition to small sample numbers for some groups, it is also difficult to parse some specific processes that drive bleaching due to confounding variables. This is demonstrated by our discussion of the spatiotemporal trend in bleaching of mouth bar sands.
Regardless of the limitations, our study is unique in the number and
diversity of samples used to test bleaching, and it therefore makes strides
toward capturing the variability of OSL signal bleaching of sediments in the
Mississippi River and its delta and thus the natural (and anthropogenic)
complexity of fluviodeltaic systems. Our results clearly show that bleaching
of fluviodeltaic sediment can vary greatly by time, space, grain size,
and/or depositional environment, even within a single river-delta system.
Had our study only investigated a small subset of the data herein, we could
have easily arrived at different conclusions with regard to bleaching by
grain size. For example, a comparison of 75–125
Despite the inherent complexity of river networks, the science of luminescence dating is advancing through the use of luminescence signals to fingerprint fluvial sediments and reconstruct the routing of grains (e.g., Sawakuchi et al., 2018; McGuire and Rhodes, 2015). Our study demonstrates how luminescence signal bleaching may link to transport histories and/or the fluvial conditions under which grains are deposited and gives insight into the last light exposure of sediment grains within a river channel. Such information is of high relevance to sustaining the Mississippi Delta and perhaps other deltas by engineered river diversions (e.g., CPRA, 2017) because the success of diversions will rely in part on their feeder channel's ability to mine sediment from suspended and/or bedload material within the river. For example, it has been proposed that locating diversions near sandbars on the riverbed may maximize sand capture, thereby supplying the coarsest material needed to build a solid substrate of new land (e.g., Allison and Meselhe, 2010; Nittrouer et al., 2012; Meselhe et al., 2012). The residence times of riverbed bars and their ability to recharge are not well known, yet they could be probed through estimates of the OSL residual doses of the bar sands. The methodology applied herein may thus provide a foundation for future work relevant to delta restoration.
This study presents the first application of a recently proposed and tested method to quantify bleaching of the OSL signal of sand grains, making use of the difference in doses obtained through central and minimum age models. We also test the bleaching of fine-grained sediments through measurement of modern analogs and through sand–silt pairs isolated from the same deposits. Through our analysis of a large and diverse dataset of Mississippi River bedload and suspended load sediments, as well as sediments of Late Holocene Mississippi Delta deposits, we arrive at the following conclusions.
OSL signal bleaching of sand within a large delta can be highly temporally and/or spatially variable. Inferences about the degree and mechanisms of bleaching of fluviodeltaic sediments should therefore be drawn from large datasets. For dating purposes (e.g., establishing overdispersion of well-bleached samples for age model input), it is best if such datasets include samples from the time interval, depositional environment, and region of interest.
Quartz silt extracted from Late Holocene Mississippi Delta deposits and from suspension within the modern Mississippi River were generally well bleached, consistent with previous findings in other large fluviodeltaic systems. The upwelling of turbid water may therefore play a significant role in bleaching of suspended sediment in large rivers, and quartz silt should be further tested as a viable option for luminescence dating in megadeltas.
Although there are many unknowns with regard to processes that drive the luminescence signal bleaching of river sediment, our research demonstrates the potential of this rapidly advancing tool to yield insight into the routing of sediments through fluvial systems, which is of relevance to delta restoration initiatives.
Bootstrap scripts for age modeling are available through the Netherlands
Centre for Luminescence dating website
(
This research is based on archival data; references are made to original publications.
The supplement related to this article is available online at:
The research was designed by ELC and JW. Analyses were conducted by ELC, with input from JW. Both authors contributed to the interpretation of results and paper synthesis.
The authors declare that they have no conflict of interest.
We thank Mead Allison and Michael Ramirez for providing information regarding river conditions during sampling of the modern river sediments and for enabling their collection. We thank Susan Packman, Mhairi Birchall, Zhixiong Shen, and Barbara Mauz for laboratory support. This paper benefitted from reviews by Alastair Cunningham and Sebastian Kreutzer. The work was improved by comments on an earlier draft by Torbjörn Törnqvist, Steve Goodbred, Mead Allison, Barbara Mauz, and Zhixiong Shen, as well as by discussions with Tony Reimann and participants at the 2017 LED conference.
This paper was edited by Andreas Lang and reviewed by Alastair Cunningham and Sebastian Kreutzer.