Supplementary material to “Is It Feasible to Build New Land in the Mississippi River Delta?”

Published 20 October 2009

Wonsuck Kim and David Mohrig, Department of Geological Sciences, University of Texas at Austin

Robert Twilley, Department of Oceanography and Coastal Sciences, Louisiana State University, Baton Rouge

Chris Paola, Department of Geology and Geophysics, University of Minnesota, Minneapolis

Gary Parker, Department of Civil and Environmental Engineering and Department of Geology, University of Illinois, Urbana-Champaign

Citation:

Kim, W., D. Mohrig, R. Twilley, C. Paola, and G. Parker (2009), Is it feasible to build new land in the Mississippi River delta?, Eos Trans. AGU, 90(42), 373–374. [Full Article (pdf)]

The Land-Building Model

The land-building model simulates the evolution of a prograding delta with a topset and foreset advancing into standing water. An elaboration of the basic principles of the model can be found in several previously published papers [e.g., Parker et al., 1998a; b; Kostic and Parker, 2003a; b; Swenson et al., 2000; Parker et al., 2008a; b]. The model captures space- and time-averaged characteristics of delta evolution. More specifically, it calculates the characteristics of an “effective channel” that amalgamates the major active channels during floods, but the channel is not specifically located. Instead, it is assumed to migrate, avulse, and flood in such a way as to maintain overall radial symmetry of the delta as it builds land. The model thus yields the average downstream bed slope and elevation profiles of the delta, the height of the foreset, position of the shoreline and delta area as functions of time. The model has the following features.

Delta opening angle and vertex position are specified.
Flood discharge is abstracted into an effective, morphologically active flood flow continued for a specified fraction of time per year, using the method of Paola et al., [1992]. This discharge is assumed to be the effective bankfull, or channel-formative discharge for the effective channel.
The total bed material (sand) transport rate is computed using the Engelund-Hansen equation [Engelund and Hansen, 1972]. The coefficient has been adjusted based on model runs for the Wax Lake Delta.
Sediment mass balance is satisfied rigorously via the Exner equation of sediment conservation.
Sand is deposited in the virtual channel, but the implicit shift of this channel spreads the sand across the entire delta.
Mud is carried as wash load in the virtual channel, but can deposit overbank. The zone of overbank deposition is implicitly spread across the entire delta top as the “effective channel” avulses/migrates.
For each unit of sand deposited within the delta, a specified unit of mud is deposited with it. The relevant coefficient is obtained from field data.
Sand that reaches the downstream end of the delta is deposited on a foreset, the slope of which is specified from field data. This deposition drives delta progradation.
The basement over which the delta advances can be horizontal, or can have a specified slope that represents an average of the actual bathymetry.
The basement can be allowed to subside at a prescribed rate. The subsidence is assumed to be spatially uniform.
The dimensions of the virtual channel, and in particular its width, are computed via a closure method using a Chezy flow resistance equation, the above-mentioned bed material load equation, and a specified, field-verified bankfull Shields number characterizing channel mobility [Parker et al., 1998a].
The flow in the effective channel is computed using a normal-flow formulation with mean sea level as the downstream datum. Mean sea level is allowed to rise at a specified constant rate for each model run.
The model allows for an engineered guide channel of specified width and length to carry the water and sediment to the vertex of the growing delta. The hydraulics and sand transport in the guide channels are calculated using the same relations as those for the virtual channel on the delta.

Input Variables

The land-building model was calibrated and verified against the observed evolution of the Wax Lake (WL) Delta since 1980. It was then applied to two adjacent diversions of the Mississippi River below New Orleans, one to the southwest into Barataria Bay (BB) and the other to the northeast into Breton Sound (BS), both for 100 years starting in 2010. The input parameters and justifications are given in Table 1.

Input parameters model

¹ WL: Based on effective flood discharge in the Upper Atchafalaya River with the assumption that 41% of the floodwater enters the Wax Lake Outlet based on gage records at Atchafalaya Simmesport and Wax Lake Outlet Calumet [Wright and Parker, 2005]; BB and BS: Effective flood discharge in the Lower Mississippi River [Wright and Parker, 2005].

² Values include suspended mud and sand, including sand bedload. The annual load is carried only during floods. The two values for WL are based on the assumption that 30% (low) or 45% (high) reported in Roberts et al. [2003] of the flood flow of the Upper Atchafalaya enters the Wax Lake Outlet. The numbers for BB and BS correspond to the values for the Lower Mississippi estimated in the text [Allison et al., 2000; Horowitz, 2006; Nittrouer et al., 2008], from where the floodwater is assumed to be diverted.

³ 17% of the suspended load is sand [Allison et al., 2000], the sand bedload is equal to 1.6% of the suspended load [Nittrouer et al., 2008].

⁴ The value for the Upper Atchafalaya [Wright and Parker, 2005] is applied to WL; the corresponding value for the Lower Mississippi is applied to the flow diverted to BB and BS.

^{5, 6} All the floodwater in the Wax Lake Outlet goes to WL. Only 45% of the floodwater in the Lower Mississippi is assumed to be diverted; this is split equally between BB and BS. Such a diversion leaves 14,150 m³/s or 500,000 ft³/s in the main-stem Mississippi River during floods to allow for navigation.

⁷ The value of 0.49 for WL corresponds to a fraction of sand in WL deposit of 0.67 [Majersky et al., 1997]. In the model it is assumed that all the sand is captured in the delta, and the amount of mud captured is equal to a fraction of 0.49 of the sand, so that the overall sediment trap efficiency is 0.27. Because WL faces the open shelf, but BB and BS are in more protected zones, a higher value, i.e. a reasonable estimate of 1 is used for unit wash load deposited per unit sand there, based on personal communications from H. Roberts, Louisiana State University (emeritus) USA and T. Törnqvist, Tulane University, USA. This yields an overall trap efficiency of 0.37 for BB and BS.

⁸ WL [Dumars, 2002]; BB and BS: Value in the Lower Mississippi near the diversions [Nittrouer et al., 2008].

⁹ The value for quartz has been used.

¹⁰ The value for bay mud and sand bars [Meckel et al., 2006; Meckel et al., 2007].

¹¹ Estimate for large, low-slope sand-bed streams [Parker et al., 2008a]

¹² It is assumed here that the prodelta can have a layer of high-porosity mud, which is rapidly compacted on a one-time basis as the delta foreset propagates over it. In the case of BB and BS, the layer is assumed to be 1.45 m thick [Morton et al., 2005] with a porosity of 0.78 [Meckel et al., 2006], which compacts on a one-time basis to produce the indicated subsidence.

¹³ Initial sea level is set at zero.

¹⁴ WL [Roberts et al., 2003]; BS and BB: Estimated using the National Land Cover Data (NLCD) 2001 Elevation and Bathymetry Data.

¹⁵ WL: As of 1980 [Majersky et al., 1997]; BS and BB: Arbitrarily chosen short distances to start the model.

¹⁶ Estimated using relations of Parker et al. [2008a].

¹⁷ WL [Roberts et al., 2003]; BS and BB: NLCD 2001 Elevation and Bathymetry Data.

¹⁸ WL [Wellner et al., 2005]; BS and BB: Estimated based on the dip section of the Mississippi River Delta [Coleman, 1988; Gould, 1970].

¹⁹ WL: From satellite images; BB and BS: Maximum space-filling value.

²⁰ WL: Adopted middle value; BS and BB: Low value, middle value and high value, as justified in the main text.

²¹ WL: Adopted middle value; BS and BB: Low value, middle value and high value, as justified in the main text.

²² WL, BB and BS: Estimated using relations of Parker et al. [2008a].

²³ WL: Measured from Wellner et al. [2005]; BS and BB: Assumed values for a short channel intended to maintain pathway from diversion structure on Mississippi River to the delta vertex.

²⁴ WL: 25 km reach of the Wax Lake Outlet; BS and BB: Assumed values for a short channel intended to maintain a pathway from diversion structure on Mississippi River to the delta vertex.

²⁵ WL: Date by which the delta length had reached the initial length that is given in the 15th row; BB and BS: Assumed for illustrative purposes.

²⁶ Taken from Parker et al. [2008b], based on data for large, low-slope sand-bed rivers.

²⁷ Value evaluated by calibration to the Wax Lake Delta. That is, the bed material transport rate predicted by Parker et al. [1998a] was doubled.

Full diversion

In performing the calculations of land building based on diversion of all the available sediment in the river, we have used a total suspended sediment load of 210 Mt/yr, [Horowitz et al. 2001], with 126 Mt/yr down the lower Mississippi River and 84 Mt/yr down the Atchafalaya River. Of the Atchafalaya River load, 31.5 Mt/yr is assumed to reach the Wax Lake Delta, and the remainder to reach the Atchafalaya Delta. Calculations were performed as outlined above for WL, BB and BS assuming all the sediment is diverted. Values of unit wash load deposited per unit sand were increased to model the effect of inflation of deposit thickness due to organics. This was done by assuming that fraction 0.2 of a column of sediment in the deposit consists of organic sediment. Land building in the Atchafalaya delta was estimated by prorating the adjacent WL value based on the ratio of the sediment supply.

References

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Engelund, F., and E. Hansen (1972), A Monograph on Sediment Transport, 3rd ed., 62 pp., Technisk Forlag, Copenhagen, Denmark.

Gould, H. R. (1970), The Mississippi Delta complex, in Deltaic sedimentation: Modern and ancient, edited by J. P. Morgan, pp. 3–30, SEPM Special Publication.

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