The Effect of Grain‐Size Distribution on River Delta MorphologyRebecca L. Caldwell1*, Douglas A. Edmonds1

1Department of Earth and Environmental Sciences, Boston College140 Commonwealth Ave., Chestnut Hill, MA, 02467, *rebecca.caldwell@bc.edu

Delta morphology is thought to be controlled by river discharge, tidal range, and wave energy. However, recent research has shown that sediment properties may have a stronger control on the physical processes, size, and shape of a delta than previously recognized. Recent numerical studies have begun to quantify this control, but have been limited to the effect of sediment cohesion and subsurface sediment properties in the basin. This study focuses on how properties of the grain-size distribution – the median, standard deviation, and skewness – delivered to the delta head affects delta form. To this end, we conduct numerical experiments using the morphodynamic physics-based model Delft3D. The model setup includes a river carrying constant discharge and sediment load entering a standing body of water devoid of tides, waves, and sea-level change. We conduct 24 runs varying the distribution’s median grain size from 0.01 – 1 mm, standard deviation from 0.1 – 3, and skewness from -0.7 – 0.7. Model results are insensitive to user defined model parameters and initial and boundary conditions. Our results show that of the three parameters tested, median grain size and standard deviation have the most substantial effect on morphology while skewness has little. At low median grain size and standard deviation deltas have 3-6 active distributaries that are relatively deep. The planform is elongate and deviates from a semi-circle, and the topset and delta-front have shallow gradients. Interestingly, as median grain size and standard deviation increase, a morphological transition occurs from deltas with elongate channels to ones with braided channels. Whether or not this transition coincides with the onset of braiding for upland alluvial channels remains to be seen. These braided deltas form at high median grain size and standard deviation, and are characterized by many active, shallow distributaries, a semi-circular planform, and steep topset and delta-front gradients. Our results suggest sediment properties exert control on delta morphology, and future analysis will aim to elucidate the underlying processes.

I. ABSTRACT

III. METHODOLOGY

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IV. Results

Orton, G.J., and Reading, H.G., 1993, Variability of deltaic processes in terms of sediment supply, with particular emphasis on grain size: Sedimentology, v. 40, p. 475-512

Syvitski, J.P.M., and Saito, Y., 2007, Morphodynamics of deltas under the influence of humans: Global Planet Change, v. 57, p. 261-282.

V. Analysis

VI. CONCLUSIONS / FUTURE WORK

EP21A‐0652

Low D50 and σ low topset gradient, elongate shape, fewer channels High D50 and σ steeper topset gradient, fan-like shape, more channels Skewness results (not shown) have little effect on delta morphology

Figure 5. Modeled delta morphologies that result from changes to grain‐size distribution. Images are taken when the same volume of sediment has entered the system. 

Figure 4. Example grain‐size distributions for (A) different median grain sizes (σ =1, sk=0), and (B) different standard deviations (D50= 0.1 mm, sk= 0).

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To meet our goals we numerically model delta growth, changing only the incoming grain-size distribution.We use Delft3D, a morphodynamic physics-based model that calculates:• Hydrodynamics depth-integrated Reynolds-averaged

Navier-Stokes equations• Sediment transport Van Rijn (1993), (suspended and

bedload)• Bed evolution Exner equation

The model setup consists of an initial channel (width = 250 m, depth = 2.5 m) entering a gently sloping basin, devoid of waves, tides, sea-level change, and buoyancy forces (Fig. 3).

Upstream boundary conditions include constant water discharge of 1000 m3/s, suspended sediment load of 0.1 kg/m3, and equilibrium bed load flux.

Downstream boundary conditions include uniform water surface elevations. We vary the incoming grain-size distribution in three ways: (1) median (D50) [0.01 – 1 mm]; (2)

standard deviation (σ) [0.1-4]; (3) skewness (sk) [-0.7 – 0.7]. For every D50 (Fig. 4A)

we change σ over four increments (Fig. 4B) to produce a total of 23 runs with unique combinations of D50and σ.

Average Topset Slope1. Measure equally spaced

rays from the delta head to points on the delta shoreline

2. Assume linear slopes3. Average rays to find a

representative slope

Figure 6A. Topset slope rays shown for every ~100 shoreline points. Example deltas correspond to grain‐size distributions of D50 = 0.05 mm, σ = 2 (top panel), and D50 = 0.5 mm, σ = 2 (bottom panel).

II. STATEMENT OF THE PROBLEM

Figure 1. Deltas with similar ratios of marine to fluvial energy (Mp:Rp) have different morphologies from elongate (A) to semi‐circular (B) to braided (C). Data from Syvitskiand Saito (2007) and Edmonds (unpublished).

Delta morphology has traditionally been explained by differences in river, wave, or tidal energy, yet deltas influenced by similar ratios of marine to river energy can display strikingly different morphologies (Fig. 1). This suggests that delta morphology may be controlled by additional variables. Previous research has qualitatively noted that grain size can influence delta morphology (Fig. 2), but a clear mechanistic understanding of this is lacking.

Here we quantify how changes in grain-size distribution affect delta morphology, with the intention of developing a mechanistic understanding of the morphological changes.

Figure 2. Delta morphology is related to grain size in addition to river, wave, and tidal energy. (from Orton and Reading, 1993).

As D50 and σ increase a morphological transition occurs. To quantify this we measure the following morphometric parameters:

Results suggest that changing grain-size distribution creates the following trends:

Planform Shape1. Measure distances from

equally spaced shoreline points to semi-circular shoreline of same area as delta

2. Take the root mean square of the deviations to measure how much the planform shape deviates from a semi-circle

Figure 6B. Deviation lengths shown for every ~45 shoreline points. Example deltas from Fig. 6A are shown.

Number of Channels1. Measure number of

channels along a curve that is everywhere half the distance to the shoreline from the delta head

Figure 6C. Cross‐section locations used for channel count, corresponding to half the distance to the shoreline. Example deltas from Fig. 6A are shown.

Average Topset Slope

y = 0.611x + 0.0002R² = 0.6462

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Figure 8. Plot of observed topset slopes from model results against predicted topset slope.

Topset slope increases more strongly with respect to D50 and than with respect to σ (Fig. 7).

Interestingly, a deviation from this trend occurs in deltas built by grain-size distributions of intermediate D50 (0.05 – 0.25 mm) (Fig. 7).

We use normal flow equations and a sediment transport relation to predict slope as a function of grain size (Fig. 8).

A reasonable correlation (R2 = 0.6462) between modeled and predicted slopes suggests the change in delta slope with respect to incoming grain-size distribution is largely due to an increase in D50.

Figure 7. Measured topset slopes (A) contoured in the D50 vs. σ parameter space, and (B) superimposed on the images of modeled deltas.

Our results suggest incoming grain-size distribution exerts a substantial control on delta morphology. This effect is evident in the following morphometric parameters:• An increase in topset slope is related to larger

median grain size.• Elongate planform shapes are related to

smaller median grain size while fan-like shapes are related to larger median grain size.

• More channels are produced in the presence of larger median grain sizes and higher standard deviation of the distribution.

Next Steps:• Measure the same morphometric parameters

on a selection of global deltas using satellite images and available hydrodynamic and sediment data. Do similar morphological variations emerge using a large database of natural deltas? Can sediment properties accurately predict delta morphology?

• Work towards determining how grain size affects delta-building processes, and develop a mechanistic understanding of the control grain-size distribution exerts on delta morphology.

The average shoreline deviation from a semi-circle describes delta planform shape as:1. High deviation more elongate2. Low deviation more fan-like

An increase in D50 creates deltas that are more semi-circular and fan-like (Fig. 9).

Interestingly the relationship is not monotonic (Fig. 9A).

Number of channels increases more strongly with respect to D50 and than with respect to σ (Fig. 10).

The gradient in number of channels is steepest at high/low D50 (Fig. 10A).

It is unclear if the increase in number of channels (Fig. 10) corresponding to increasing D50 and σ is related to the onset of braiding due to higher slope (Fig. 7).

Planform Shape

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Figure 9. Distribution of measured deviation from a semi‐circle (A) contoured in the D50 vs. σ parameter space, and (B) superimposed on the images of modeled deltas.

Number of Channels A

Figure 10. Distribution of number of channels on center cross‐section (A) contoured in the D50 vs. σ parameter space, and (B) superimposed on images of modeled deltas.

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Mossy DeltaD50 = 0.125 mmMp:Rp = minimal

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Figure 3. Numerical model setup. Each grid cell size is 25 x 25 m. 

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