River deltas are sites of sediment accumulation along the
coastline that form critical biological habitats, host megacities, and
contain significant quantities of hydrocarbons. Despite their importance, we
do not know which factors most significantly promote sediment accumulation
and dominate delta formation. To investigate this issue, we present a global
dataset of 5399 coastal rivers and data on eight environmental variables.
Of these rivers, 40 % (
Deltas provide a variety of ecosystem services, such as carbon sequestration and nitrate removal (Rovai et al., 2018; Twilley et al., 2018), and they provide a home to close to half a billion people (Syvitski and Saito, 2007) living within large agricultural and urban centers (Woodroffe et al., 2006). Deltas form at river mouths where fluvial sediment accumulates nearshore long enough for the deposit to become subaerial. This simple view of delta formation is a statement of sediment mass balance; understanding where deltas form requires knowing how and why sediment accumulates. Sediment accumulates provided it is supplied and deposited at the coast faster than it is removed. Sediment supply and removal are chiefly determined by the river, waves, tides, rate of relative sea level change, and offshore bathymetry. To complicate matters, most of these variables can be both sources and sinks of sediment, and their exact roles in the deltaic sediment mass balance remain uncertain. Previous research suggests that rivers are almost always sources (Bates, 1953; Coleman, 1976; Wright, 1977; Syvitski et al., 2005; Syvitski and Saito, 2007). The roles of waves and tides are largely ambiguous (Nienhuis et al., 2015; Hoitink et al., 2017; Lentsch et al., 2018), though there is some evidence to suggest waves are mainly sediment sinks in the delta formation process (Fisher, 1969; Anthony, 2015). The bathymetric characteristics of the offshore basin determine the nearshore hydrodynamics, wave power, and structure of the turbulent jet, which in turn influences sediment deposition patterns and delta formation (Fagherazzi et al., 2015; Jiménez-Robles et al., 2016). Sea level is also an important part of delta formation, and we know that slower rates of sea level rise promote delta formation (Stanley and Warne, 1994; Porebski and Steel, 2006; Paola et al., 2011).
Despite these efforts, we do not fully understand how these different controls combine to create river deltas. We know the conditions for delta formation are not easily met – pick nearly any marine shoreline on Earth and of the river mouths that intersect the coast, only some will have a delta. Previous studies on delta formation (Wright et al., 1974; Audley-Charles et al., 1977; Milliman and Syvitski, 1992; Syvitski and Saito, 2007; Nyberg and Howell, 2016) focused on large-scale patterns and concluded that major modern delta locations are influenced largely by tectonic margin type and drainage patterns. While useful, these datasets were biased toward the largest and most populated deltas. Expanding the prediction effort to deltas of all sizes is a logical next step, especially because smaller deltas are thought to be more resilient to rising sea levels (Giosan et al., 2014).
In addition to expanding the range of delta sizes to understand the controls on delta formation, we need to consider cases in which delta formation is suppressed. In this paper we investigate why some rivers form deltas and others do not. Understanding conditions for modern delta formation should also help exploration for ancient deltaic deposits, which requires predicting where deltas might form under past environmental conditions (Nyberg and Howell, 2016). Similarly, as research moves toward delta risk assessment due to global environmental change (Tessler et al., 2015) and improving efforts to build new deltaic land (Kim et al., 2009), we must understand how different environmental variables govern delta formation. For example, understanding the conditions for delta formation would help restoration efforts that seek to build new deltaic land in places like the Mississippi River Delta (Paola et al., 2011; Edmonds, 2012; Twilley et al., 2016).
To address these issues, we developed a global dataset that includes the
locations of 5399 coastal rivers, information on whether they form deltas
or not, and the environmental variables that could influence delta
formation. We use global datasets of coastlines (Dürr et al., 2011;
Nyberg and Howell, 2016), sediment and water (Syvitski and Milliman, 2007;
Milliman and Farnsworth, 2011), wave climate hindcasts (Tolman, 2009; Chawla
et al., 2013), a tidal inversion model (Egbert and Erofeeva, 2002), ocean
bathymetry data (Amante and Eakins, 2009), and the rate of sea level change
(
River deltas are fundamentally systems of sediment accumulation and distribution at the coastline. Accordingly, we identify coastal deltas by distinguishing geomorphic expressions of sediment accumulation and distribution at locations where rivers meet the coast. We consider a river to have formed a delta at the coastline if the river-mouth area contains an active or relict distributary network (Fig. 1e), ends in a subaerial depositional protrusion from the lateral shoreline (Fig. 1d), or does both (Fig. 1c). Distributary networks are an expression of sediment deposition and distribution (Edmonds et al., 2011) and we identify them by the presence of one or more channels that bifurcate and intersect the coast at different locations. We include relict channels, where they are clearly visible in imagery and connect to the main channel, because they are evidence of sediment distribution and accumulation through avulsion (Slingerland and Smith, 2004). We do not include channels that bifurcate solely around non-deltaic topographic highs. Our second criterion is oceanward-directed shoreline protrusions. We classify a protrusion as deltaic if it has a relatively smooth depositional shoreline, as opposed to rough shorelines associated with rocky coasts (Limber et al., 2014), and if it extends more than approximately five channel widths oceanward relative to the position of the regional shoreline. We map only protrusions that are associated with the river, ignoring protrusions that may exist near the channel mouth that we judge to be preexisting undulations in the shoreline. Examples of this include promontories associated with preexisting geology or depositional protrusions created by other processes, such as wave-driven sediment transport (Ashton et al., 2001). Our delta identification method does not account for deltaic deposition with no geomorphic signature, such as a single-channel delta infilling a drowned valley that produces no protrusion from the regional shoreline. Although such features may be considered deltaic, we cannot unambiguously identify them as deltas based on aerial imagery alone and we do not include them in the dataset.
Examples of
We applied the preceding criteria to a scan of marine coastlines, including
most open-ocean coasts and the Black Sea, using Google Earth. First, we
identified all rivers with width
We mapped rivers and deltas on the coastlines of Earth's continents and large islands (Fig. 2). We exclude small islands where rivers large enough for inclusion are rare and it is difficult to obtain environmental data. Thus, large islands, such as Papua New Guinea and Fiji, were included but not all the associated smaller islands. Coastlines dominated by fjords (as determined using Dürr et al., 2011) were not included because offshore glacial over-deepening and protection from coastal waves and tides make their comparison to most of the world's coastal deltas difficult. Ephemeral rivers in arid regions were included in the dataset, though the rivers in these regions are often difficult to identify due to poor imagery and difficulty distinguishing the channel banks when they are dry. If a clear distinction was not possible, the river was not included in the dataset. Thus, the total count of rivers and deltas in arid regions should be considered a minimum. Finally, we did not include river channels that do not clearly reach the coast to avoid conflating alluvial fans with deltas.
Global distribution of coastal
For each river we marked the latitude and longitude of the main river mouth (Fig. 1, RM) (Table S1 in the Supplement). For rivers without a delta, this is the location where the river meets the coastline (Fig. 1a), and for rivers with deltas, this is the location of the widest river mouth in the distributary network (Fig. 1c–e). For rivers sheltered by barrier islands or rocky islands, we mark the river mouth landward of those obstructions.
To determine controls on delta formation we also compiled data on eight environmental variables (Table 1). We classify the environmental variables into two groups: (1) upstream variables include water and sediment supply from the river, sediment concentration, and the drainage basin area; (2) downstream variables include wave height, tidal range, bathymetric slope immediately offshore of the river mouth, and the rate of sea level change. We use modern data collected for each of these environmental variables, even though some deltas may have initially formed under different conditions 6000 to 8500 years ago as sea level rise slowed after deglaciation (Stanley and Warne, 1994). We assume that the current river delta (or lack thereof) is adapted to the modern environmental variables because scaling analyses suggest that the diffusive response time of river delta deposition and wave reworking is on the order of 100–1000 years (Jerolmack, 2009; Nienhuis et al., 2013). Of course, the diffusive response time depends nonlinearly on delta size, so larger deltas may still be adapting to changing environmental variables.
Notably absent in the collected environmental variables are tectonic data. At present, there are no globally available measurements of tectonic activity (e.g., uplift). However, we consider some of the variables to be reasonable proxies for tectonics. For instance, models predicting sediment flux to the ocean represent tectonics in the form of basin area (Syvitski and Morehead, 1999; Syvitski and Milliman, 2007). We also include bathymetric slope, which is a rough proxy for tectonics, because on average tectonically active margins have steeper slopes than passive margins (Pratson et al., 2007).
Independent variables: upstream and downstream environmental variables.
We compiled the four upstream variables from the global river dataset of
Milliman and Farnsworth (2011) (hereafter referred to as MF2011). We matched
rivers in this dataset with entries in MF2011 based on geographic proximity
or by the river name. If neither matching method yielded a confident result,
the MF2011 data were not included in this study. If two or more rivers in
the MF2011 dataset combine to make one river in this study's dataset, the
data from all relevant MF2011 rivers are included. In cases in which matches
were found, we included the river ID(s) from MF2011 in our dataset
(Table S1). Our dataset includes 1217 MF2011 rivers,
representing 1158 entries in our dataset; 54 entries contain 2 or more
MF2011 rivers, and in those cases we added the MF2011 values together to
form one value for the river mouth or delta. There are 314 MF2011 rivers not
included in this dataset because they are too small (
Water discharge (
Sediment discharge (
We also include upstream drainage basin area (
Four downstream variables are included in this dataset. Annual significant
wave heights (
Median tidal ranges (
Receiving-basin bathymetry is an important attribute of delta formation
because it sets the size and shape of the volume to be filled from a mass
balance perspective and influences the hydrodynamics (Jiménez-Robles
et al., 2016; Carlson et al., 2018). The size of the basin could be
characterized by the average depth, whereas the shape is most simply
characterized by the bathymetric slope. In most cases, we do not know basin
depth prior to delta formation, and current depths offshore of deltaic river
mouths will be deeper than the initial depths if the basin has
offshore-dipping bathymetric slopes. Thus, instead of using depth, we
characterize the receiving basin with bathymetric slopes. Bathymetric slopes
(
The rate of sea level change is calculated from AVISO (Archiving, Validation and
Interpretation of Satellite Oceanographic data,
Our mapping reveals that there are 5399 coastal rivers with widths greater than
50 m, and 2174 of those rivers (
River deltas are not distributed evenly on coastlines and there are
locations on the world's coastlines where deltas are unusually common (Fig. 2). These “delta hotspots” occur primarily in Southeast Asia (dashed box
Fig. 2b). Notably, these areas are also densely populated with rivers (Fig. 2a), though river abundance does not always equate to delta abundance. For
example, East Asia has a high river density but low delta density (black box,
Fig. 2b). Similarly, along the west coasts of central and southern North
America (from 5 to 45
Binning these data by latitude reveals preferential locations of rivers and
deltas (Fig. 3). The largest numbers of rivers and deltas occur roughly from
Histograms showing the latitudinal distribution (3
To determine which environments promote delta formation, it is perhaps most
instructive to observe locations where the likelihood for rivers to create
deltas is highest. Delta likelihood (
These latitudinal zones, where rivers are more likely to create deltas,
coincide with peaks in environmental variables that influence delta
formation. Both
Latitudinal variation of the independent variables used in this
study. All panels show the median value for 3
We explore controls on delta formation by analyzing how the likelihood of a
river creating a delta varies with each environmental variable. River mouths
and deltas have statistically different population distributions for seven
of the eight environmental variables (all but
Statistical differences between rivers with no deltas and rivers
with deltas. Percentages are calculated relative to the total number of
rivers with no deltas (3225) and with deltas (2174).
Delta likelihood (
Differences in upstream environmental variables for rivers with and without deltas. Scatter plots (top of each panel) of delta likelihood, defined as the number of rivers with a delta relative to the total number of rivers in that interval. Histograms (bottom of each panel) binned into equal log-spaced intervals. Gray boxes outline ranges represented by 1 % or less of the total sample number.
Rivers are less likely to create deltas where
Differences in downstream environmental variables for rivers with
and without deltas. Scatter plots (top of each panel) of delta likelihood, defined
as the number of rivers with a delta relative to the total number of rivers in that
interval. Histograms (bottom of each panel) binned into equal log-spaced intervals.
Gray boxes outline ranges represented by 1 % or less of the total sample
number. Sea level change plot and histogram
To quantify the relative importance of the environmental variables for delta
formation, we develop an empirically derived logistic regression. The result
of a logistic regression is a statistical model that predicts a dichotomous
outcome (in this case, a river creates a delta, or it does not) based on
multiple independent variables. This dataset contains eight total
independent variables collected on most rivers: four are upstream
variables (
The data meet the assumptions of binary logistic regression because the
dependent variable has two mutually exclusive outcomes and the sample size
is large (45 samples or more per independent variable). Additional
assumptions that the data must meet include having little to no
multicollinearity and no outliers. We tested for multicollinearity by
calculating the Pearson correlation coefficients (
The binary logistic regression between the probability that a river will
create a delta and the eight environmental variables yields the following
log odds relationship:
Thus, the combination of environmental variables that comprises the right
side of Eq. (1) predicts the log odds that a river will form a delta.
When tested using the validation subset, Eq. (1) has a 74 % success
rate at predicting delta presence (Fig. 7), wherein
Scatter plot of measured versus predicted delta formation.
Eq. (1) was used to calculate the predicted probability of delta formation,
This empirically derived relationship can be used to calculate the
probability that a certain combination of the most important environmental
variables will form a delta. For example, using environmental variable
values for the Godavari River in the right-hand side (RHS) of Eq. (1)
results in
We have considered the relationships between eight environmental variables
and delta formation. However, determining which variables are most dominant
is not straightforward. After all, most combinations of environmental
variables that exist globally completely suppress delta formation (60 % of
the rivers included in this dataset do not have a delta). Our likelihood
analysis shows that deltas are more likely to form at river mouths with
large water discharge
These controls on delta formation explain the first-order latitudinal variations
observed in Figs. 3 and 4. For example, the peaks in water and sediment
discharge values from
Downstream bathymetric slope (
Our data suggest that deltas are fundamentally created by water and sediment discharge, whereas waves, and possibly tides, suppress delta formation. This is consistent with the notion that delta formation is the result of constructive upstream forces set by the river and destructive downstream marine forces (Fisher, 1969, Boyd et al., 1992, Anthony, 2015). This idea, initially proposed by Fisher (1969), provides a different perspective compared to the oft-cited study on delta morphology and formation from Galloway (1975). Galloway's diagram implies that deltaic formation and morphology are the result of the interplay of the river, waves, and tides. In the case of a purely wave-dominated delta, Galloway's diagram would predict a cuspate delta. Instead, our data clearly show that the most wave-dominated delta is no delta at all, consistent with other studies (Nienhuis et al., 2013; Boyd et al.,1992). This suggests to us that the concept of delta formation and morphology might be better cast as a balance between constructive and destructive forces.
If we consider the perspective that delta formation is the result of a balance between constructive and destructive forces, then new questions emerge: how do wave and tidal processes influence the ability of fluvial processes to construct deltas? How stable is the balance between a given set of constructive and destructive forces? Regarding the last question, there are examples of rapid changes in delta morphology through time, which suggests that the balance can be precarious. The Rhône River delta shifted in morphology from channel-network-dominated in the 16th century to its current wave-smoothed shape as floods and sediment loads declined during the Little Ice Age (14th–19th centuries) (Provansal et al., 2015). The Po River delta showed three morphological transitions each time the balance between river and waves changed over the last 4000 years (Anthony et al., 2014). These examples from the past should direct our attention to how the current configuration of deltas might change in the future. We know that anthropogenic climate change is changing wave conditions (Reguero et al., 2019) and humans are drastically changing water discharge and sediment flux to coastal rivers (Syvitski and Milliman, 2007). It is unclear how the coastal deltas of the world will adapt to these changes in boundary conditions. Future work would benefit from linking our empirically derived delta likelihood predictor with metrics of delta morphology to understand when morphological shifts might occur.
River deltas are the final filters of sediment before it is discharged to
the global oceans (Sawyer et al., 2015). Although only 40 % of rivers in
our dataset form deltas, our results show that 5.9 Bt yr
We also propose that our data and analyses have important implications for
resource exploration and coastal restoration. Although using Eq. (1) to
predict delta formation for modern rivers is somewhat redundant, it may
prove useful for predicting past or future delta existence. Ancient deltaic
deposits comprise significant hydrocarbon reservoirs, and provided our
analysis holds through geologic time, we could predict the presence of
deltaic deposits in the rock record if
Looking forward, this relationship can be used to predict future deltaic
formation. Global environmental change will continue to put coastal
environments at risk, largely by land loss due to accelerated sea level rise
and decreased sediment delivery to the coast. Coastal restoration and
hazard-mitigation techniques often involve the creation of new deltaic land
via controlled river diversions (e.g., Kim et al., 2009), though it can be
difficult to predict the risk related to such projects. Predictions made
using Eq. (1) can help in the decision-making process concerning setting
controllable environmental variables, such as water discharge. For example,
in a hypothetical environment where a river diversion is being considered
and the current set of environmental variables yields
Based on analysis of a new dataset comprising 5399 coastal rivers that are
at least 50 m wide, along with eight environmental variables, we find that
only 40 % (2174) of coastal rivers have deltas, and these are unevenly
distributed geographically, with delta formation being more likely in
latitudes
All data are supplied in Table S1 in the Supplement. For upstream variable values, use “M&F_ID(s)” to find in Milliman and Farnsworth (2011).
The supplement related to this article is available online at:
RLC and DAE led the organization of the study and the writing of the paper. RLC performed data analysis. SB performed tidal data compilation. CP contributed to dataset creation strategy. JHN performed wave data compilation. SR performed bathymetric data compilation. All authors contributed to dataset creation and edited the paper.
The authors declare that they have no conflict of interest.
Sea level products were
processed by Ssalto/Duacs and distributed by AVISO
This research has been supported by the National Science Foundation (grant nos. 1135427, 1426997, and 1812019).
This paper was edited by Sebastien Castelltort and reviewed by Janok Bhattacharya, Jinyu Zhang, and one anonymous referee.