River Diversions: Principles, Processes, Challenges and 

Opportunities 

A Guidance Document 

September 7, 2012 

Prepared for: 

U. S. Army Corps of Engineers 

State of Louisiana 

U. S. Geological Survey 

Prepared by: 

Robert G. Dean 

John T. Wells 

Joseph Fernando 

Peter Goodwin 
i

Table of Contents 

Executive Summary ...............................................................................................................ES-1 

1.0 Introduction ......................................................................................................................1 

2.0 Evolution Characteristics of Large Diversion Deposits...................................................3 

3.0 Variables that Impact Diversion Performance ................................................................5 

4.0 Criteria for Deposition and Stability of Diversion Deposits ...........................................7 

 4.1 Critical Shear Stress .......................................................................................7 

 4.2 Fall Velocity...................................................................................................8 

5.0 Simple Models for Scoping and Sensitivity Studies ........................................................9 

 5.1 Geometric Model 1: Truncated Cone, Uniform Depth .................................11 

 5.1.1 General ..............................................................................................11 

 5.1.2 Time to Emergence of a Subaerial Platform for a Truncated Cone ..12 

 5.2 Geometric Model 2: Uniform Width ............................................................14 

 5.2.1 General ..............................................................................................14 

 5.2.2 Time to Emergence of a Subaerial Platform for Uniform 

Width and Depth Model................................................................................. 15 

 5.3 Examples Illustrating Application of the Two Models ..................................16 

 5.3.1 Example 1. Case of Large Scale Diversion, Truncated Cone 

 Model ................................................................................................16 

 5.3.2 Example 2. Large vs. Small Diversions, Truncated Cone Model .....17 

 5.3.3 Example 3. Uniform Width and Depth Model ..................................18 

 5.3.4 Example 4. Uniform Width Model, Effect of Bottom Slope ............18 

 5.3.5 Example 5. Uniform Width and Depth Uniform Model, 

 Effect of Relative Sea Level Rise .....................................................19 

 

6.0 Guidance for Selection of Diversion Parameters .............................................................20 

 6.1 General ...........................................................................................................20 

 6.1.1 Annual Inorganic Sediment Input ...................................................21 

 6.1.2 Foreset Slope ...................................................................................22 

 6.1.3 Proportion of Diverted Material Retained ......................................23 

 6.1.4 Subsidence ......................................................................................24 

 6.1.5 Bulking Factors ...............................................................................24 
ii

7.0 Examples Illustrating Application of the Recommended Methodology ..........................25 

 7.1 Planned White Ditch Diversion .....................................................................25 

 7.2 West Bay Diversion .......................................................................................28 

8.0 The Role of Monitoring ...................................................................................................30 

9.0 Improved Method for Applying Models ..................................................... 31

10.0 Lessons From Previous Diversions ................................................................................32 

11.0 Summary and Recommendations ..................................................................................35 

 11.1 Summary of Methodology and Parameter Selection ...................................35 

 11.2 General Recommendations for Parameter Selection ...................................36 

 10.2.1 Subsidence Rates and Sediment Retention ...................................36 

 10.2.2 Delta Opening Angle and Diversion Depths ................................36 

12.0 References ......................................................................................................................37 

Appendix A: Useful Conversion Factors (Some are Approximate) and Estimates ...............A-1 

Appendix B: Time to ‘Platform Building” ............................................................................B-1 

List of Figures 

Figure Number Figure Caption Page Number 

1 Location map showing diversion locations along the main stem of the Mississippi 

River ------------------------------------------------------------------------------------------- 1 

2 Life cycle of subdelta of the Mississippi River Delta (from Wells and 

 Coleman, 1987) -------------------------------------------------------------------------------- 4 

3 Fall velocity vs. sediment diameter (from Rouse, 1937) --------------------------------- 8 

4 Definition sketch of a truncated cone in water of uniform depth ---------------------- 11 

5 Interpretation of three stages of evolution for truncated cone -------------------------- 12 

6 Non-dimensional time, t’, vs non-dimensional discharge, Q’, for truncated 

cone -------------------------------------------------------------------------------------------- 13 

7 Uniform width model. Sloping sea floor -------------------------------------------------- 14 
iii

8 Non-dimensional time, t’, vs non-dimensional discharge, Q’, for uniform width 

and uniform depth model ------------------------------------------------------------------- 15 

9 Example 1. Annual discharge of retained sediment = 3 x 106 m3/yr, initial depth of 

receiving waters = 2.0 m, elevation of horizontal portion of deposit above mean water 

level = 0.25 m, rate of relative sea level Rise = 2.0 cm/yr, foreset slope = 0.002 and delta 

opening angle = 180o

 ------------------------------------------------------------------------ 16 

10 Example 2. Comparison of subaerial areas over time for one large diversion vs two 

diversions with the same total sediment retention. Initial depth of receiving waters = 0.75 

m, elevation of horizontal portion of deposit above mean water level = 0.25 m, rate of 

relative sea level rise = 1.0 cm/yr, foreset slope = 0.002 and delta opening angle = 180o

 -------------------------------------------------------------------------------------------------- 17 

11 Example 3. Berm length, x , of deposit (see Figure 7) for diversion deposit of uniform 

width and into receiving waters of uniform depth. Annual volume of sediment retained, 

width of deposit = 2,000 m, initial depth = 1.5 m, elevation of deposit platform above 

water level = 0.25 m, relative sea level rise = 1 cm/yr. --------------------------------- 18 

12 Example 4. Comparison of subaerial areas over time for two bottom slopes. Uniform 

width, annual retention of sediment = 200,000 m3/yr, relative sea level rise rate = 1.0 

cm/yr. Initial depth of receiving waters = 0.75 m, Elevation of horizontal portion of 

deposit above mean water level = 0.25 m, foreset slope = 0.002 ---------------------- 19 

13 Example 5. Comparison of subaerial areas over time for relative sea level rise rates, 

uniform width = 2,000 m, annual retention of sediment = 200,000 m3

/yr. Initial depth of 

receiving waters = 2.0 m, elevation of horizontal portion of deposit above mean water 

level = 0.25 m, foreset slope = 0.002, bottom slope = 0 -------------------------------- 20 

14 Recommended values for foreset slopes. Values in parentheses apply to sand size 

sediment -------------------------------------------------------------------------------------- 23 

15 Preliminary recommendations for proportion of diverted material retained, FR ----- 23 

16 Preliminary recommendations for subsidence rates, Fs --------------------------------- 24 

 17 Preliminary recommendations for bulking factors, FB ---------------------------------- 25 

18 Results from application of uniform width method to planned White Ditch 

 Diversion --------------------------------------------------------------------------------------- 28 

19 Results from application of truncated cone method to West Bay Diversion --------- 30 
iv

B-1 Non-dimensional time, t’, vs non-dimensional discharge, Q’ for truncated cone 

 Model ----------------------------------------------------------------------------------------- B-2 

B-2 Non-dimensional Time, t’, vs non-dimensional discharge, Q’ for uniform width 

model ----------------------------------------------------------------------------------------- B-3 

List of Tables 

Table Number Table Caption Page Number

1 Comparison of sediment transport by river diversions on the basis of equations herein and 

 other estimates ................................................................................................................22 

2 Summary of recommended input values for White Ditch and West Bay Diversions ...26 

3 Calculations to time of emergence for various sediment delivery estimates for the 

 planned White Ditch Diversion .....................................................................................27 

4 Calculations of time of emergence for various sediment delivery estimates for the 

 West Bay Diversion ........................................................................................................29 

5 Background on other diversions ....................................................................... 32 
ES‐1

River Diversions: Principles, Processes, Challenges and Opportunities 

A Guidance Document 

Executive Summary 

This Guidance Document provides a framework and rational basis for the preliminary design of 

river diversions and the selection of key design parameters that will impact their performance. 

The document is based on the assumption that river diversions are, and will continue to be, one 

of the principal tools for building new land in coastal Louisiana, and that the significant gaps in 

our understanding of performance must, and almost certainly will, be addressed through 

application of numerical models. The guidance presented in this document is based on 1) the 

body of published and unpublished literature that draws from the knowledge and experience of 

others, 2) the results of simple analytical models that were developed specifically for this 

document, and 3) our own knowledge, insight and application of best professional judgment. 

River diversions, if successful, will create new land that mimics scaled-down versions of natural 

delta lobes. The evolution of these features as they occur in nature, referred to in the literature as 

subdeltas or bay-fill deposits, is well documented. It begins with a break or crevasse in a major 

distributary natural levee during flood stage, enlarges as flow increases through successive 

floods, reaches a peak of maximum discharge and deposition, then wanes and becomes inactive, 

all within a time frame of decades to centuries. The performance of river diversions will be 

controlled by numerous factors that can be broadly categorized as 1) basin geometry, 2) sediment 

characteristics, 3) biological factors, 4) water motion including turbulence, and 5) design and 

operational strategies. Included in these broad categories are important variables including water 

depth, sea level rise, subsidence, input of sand, impact of storms and major floods, and the role 

of vegetation in changing bulk density and stabilizing the deposits. 

Two geometric models were developed to allow calculation of future performance of river 

diversions. These geometries, a truncated cone and a uniform width geometry, assume a constant 

discharge of sediment into the receiving basin and thus avoid many of the complexities of the 

evolutionary processes. Model results from both geometries show a clear life cycle of growth 

and deterioration in a diversion that experiences relative sea level rise and, under certain 

combinations of relative sea level rise, depth of receiving waters and sediment discharge rate, 

situations in which a subaerial platform will never form. A comparison of subaerial deposits in 

larger versus smaller diversions, assuming the same total sediment discharge in both cases, 

reveals that the total subaerial land area for the larger diversions is substantially greater than the 

sum of the two volumes of the smaller diversions. Model results have been used to illustrate 

through examples, the effect of bottom slope and sea level rise on diversion performance. 
ES‐2

Preliminary recommendations have been made for the selection (quantification) of diversion 

parameters to be used in the models. These include annual sediment input, proportion of 

sediment retained in the diversion deposit, sediment bulking factor, foreset slope, and subsidence 

rate. Other required input parameters are considered to be User-specified, namely average 

diversion water discharge, initial depth of receiving waters, bottom slope, deposit angle or width, 

and future sea level rise. Using recommendations in the document that were taken from a 

synthesis of data in the literature, calculations for time to emergence for various sediment 

delivery estimates were made for the White Ditch Diversion and the West Bay Diversion. 

Estimates can vary widely depending on foreset slope and whether sediments include a mix of 

sand, silt and clay (versus sand only), but values in the range of 5-15 years for White Ditch and 

11-13 years for West Bay are considered to be reasonable. 

This Guidance Document also includes general recommendations for selection and utilization of 

diversion sites: 1) select sites that, based on all available evidence, are in areas of low 

subsidence; 2) select sites that are likely to have very high trapping efficiency; 3) select sites that 

are less than 2 m in depth; 4) select sites that have very low bottom gradients; 5) implement a 

well-thought-out monitoring plan to be part of each diversion project; 6) apply adaptive 

management as new information and understanding becomes available from monitoring; 7) 

recognize that diversions will have a life cycle and are not permanent features; and, 8) recognize 

and model insofar as possible the effects on navigation that will likely result from large 

diversions. 

Appendix A presents useful conversion factors and estimates of Mississippi River average 

annual water and sediment discharges.
1

River Diversions: Principles, Processes, Challenges and Opportunities 

A Guidance Document 

1.0 Introduction 

River diversions are one of the fundamental tools available for coastal restoration in Louisiana. 

Under certain scenarios, they offer an efficient and effective means of building new land, 

providing a substrate for wetland growth and an opportunity for enhancement of ecological 

diversity. We have conducted an extensive literature survey of the state of knowledge of 

diversions with regard to basic principles and processes, and have examined the efficacy of 

diversion projects at multiple scales on the Louisiana coast. Although much has been written on 

river diversions, and indeed much is known from the myriad of studies over the past 30 years, 

some significant gaps in our understanding remain, perhaps most notably the overarching 

uncertainty in forcing landscape perturbations of the scale of large river diversions. Basic 

principles and processes of how diversions function are discussed in this document, including the 

role of sea level rise and subsidence, sediment composition and quantity, effects of receiving 

basin characteristics, and impacts of river flow. Challenges and opportunities for using 

diversions as a tool in the restoration of coastal Louisiana are also presented, and we end by 

providing a set of recommendations that focus on applicability and limitations of our guidance, 

and the importance of sensitivity studies. Figure 1 presents locations of existing and planned 

diversions along the main stem of the Mississippi River. 

Figure 1. Location map showing diversion locations along the main stem of the Mississippi 

River. 
2

At first, diversions may seem an obvious and relatively straightforward approach to restoration in 

Louisiana: they reconnect the Mississippi River to the surrounding wetlands, removing the 

hydrologic disconnection that began more than a century ago, thereby allowing nature, largely 

unaided, to use its own “raw materials” to create new land. However, a closer look reveals that 

there are many complex issues associated with large river diversions: 1) Lack of “textbook” 

design criteria given that, with the exception of the West Bay project in 2003, previous 

diversions have been focused primarily on introduction of freshwater rather than sediment. 2) 

Unintended impacts on the main stem of the river, primarily as a result of shoaling that may 

affect navigation and escalate project costs. 3) Uncertainty in subsidence leading to considerable 

controversy in subsidence rates, their temporal and spatial variations, and their relevant driving 

forces. 4) Limited predictive capability for land growth because of the general lack of 

understanding of the very factors that are discussed in this guidance document. 5) Unintended 

and potentially negative impacts from the freshwater introductions that co-occur with the 

introduction of sediments. 6) Societal and economic issues associated with competing 

stakeholder interests, projects costs and tradeoffs, and effectively communicating expectations.

7) Inaction because of the above issues, leading to the likelihood that actual addition of 

significant new land from diversions is still several decades away. 

Virtually all of the above questions and concerns must, and almost certainly will, be addressed 

through application of numerical models or, in some cases, laboratory models. Many currently 

exist, including: simulation of delta formation on geological time scales (Seybold et al., 2007); 

simulation of birdsfoot deltas on 100 to 1,000-yr time scales (Kim et al., 2009; Seybold et. al., 

2009); simulation of individual landform features such as channel networks and river mouth bar 

formation on time scales of years to decades (Edmonds and Slingerland, 2007; Wolinsky et al., 

2010); and, simulations that relate delta form to variations in sediment texture (Edmonds and 

Slingerland, 2010). In contrast, we offer in this document a modeling approach that utilizes 

simple analytical models specifically for the purpose of guiding design and preliminary 

evaluation by examining interrelationships among key variables. 

The guidance presented herein is based on 1) the considerable body of published and 

unpublished literature that draws from the knowledge and experience of others, 2) the results of 

the simple analytical models that were developed specifically for this document, and 3) our own 

knowledge, insight, and application of best professional judgment. We approach the topic of 

river diversions from the standpoint of voicing considerable urgency and the need for action in 

the very near future, yet at the same time, recognizing that it would be presumptuous to suggest 

that this guidance document furnishes definitive answers to complex questions that will require 

additional analysis. 
3

2.0 Evolution Characteristics of Large Diversion Deposits 

River diversions, if successful, will create new land that mimics scaled-down versions of natural 

delta lobes, referred to in the literature as subdeltas or bay-fill deposits. Within a major delta 

lobe, subdeltas and smaller crevasse-splay deposits fill the innumerable shallow bays that flank 

the deltaic distributaries with sedimentary sequences that are typically less than 10 m thick but 

with subaerial expressions at maximum development that may reach 300 km2 or more. The 

evolution of these deposits on the lower Mississippi Delta, first illustrated by Welder (1959) and 

Coleman and Gagliano (1964), is now relatively well understood (Wells and Coleman, 1987; 

Coleman, 1988; Wells, 1996; Roberts, 1997; Coleman et al., 1998) and can serve as a 

geomorphic and sedimentologic model for creating new wetlands from river diversions (Davis, 

2000; Allison and Meselhe, 2010). 

A subdelta or bay-fill deposit is a sequence that forms initially from a break or crevasse in a 

major distributary natural levee during flood stage, enlarges as flow increases through successive 

floods, reaches a peak of maximum discharge and deposition, then wanes and becomes inactive 

(Coleman et al., 1969). As a result of high subsidence rates by compactional dewatering, an 

abandoned subdelta is gradually inundated by brackish water and reverts to an open-bay 

environment, thus completing one sedimentary cycle of infilling and abandonment that may last 

150-200 yr (Wells, 1996). Smaller crevasse-splay deposits that are associated with overbank 

flooding during very high discharge years also create new land but rarely last more than 10-15 yr 

and, during that time, will deposit sedimentary sequences on the order of 3 m thick covering 

areas of 12-15 km2 (Coleman, 1988). 

Since the mid to late 1800s, four subdeltas have together formed the sedimentary framework for 

essentially all of the wetlands in the modern birdsfoot delta and, prior to that, similar features 

undoubtedly provided the surface expression of this and other major delta lobes that were active 

during the Holocene. Analysis of the subdeltas from maps, charts and aerial photographs (Wells 

and Coleman, 1987) revealed an orderly, almost predictable life cycle, with average and 

maximum rates of subaerial growth that ranged from 0.8-2.7 km2

/yr and 1.1-7.0 km2/yr, 

respectively (Fig. 2). Average and maximum rates of deterioration were on the same order as 

rates of growth, typically several km2/yr even though the sediment volumes in the subdeltas 

continued to increase. At the time of the analysis (ending in 1980), the volumes of sediment 

deposited in the subdeltas had averaged 4-26 x 106

 m3/yr, and the Mississippi Delta had acquired 

a total of ~7000 x 106

/m3 of new sediment. 
4

Figure 2. Life cycle of subdeltas of the Mississippi River Delta (from Wells and Coleman, 1987). 

During the progradational phase of development, subdelta growth begins after crevasse 

development, but not at a constant rate. This is because of the uneven distribution of coarse 

sediment, which is deposited initially only in the vicinity of the natural break in the levee. Finegrained sediments are transported farther into the bay and build up a platform for future 

progradation and channel development. At some point in the subaqueous infilling process, 

usually after 10-15 years, major channels become established and a well-organized pattern of 

bifurcations becomes evident. It is only after the development of a well-defined channel pattern, 

hence sediment delivery network, that subaerial growth begins to increase rapidly. As 

progradation and areal extent of the subdeltas increases rapidly, so does the growth of wetlands, 

which form a cap on the underlying sedimentary deposits. Patterns of delta growth in the new 

Atchafalaya and Wax Lake deltas indicate that, after an initial period of channel extension and 

bifurcation around the river-mouth-bar deposits, increases in delta area occur primarily from 

fusion of sand-rich lobes by channel filling and upstream lobe growth (Roberts, 1997). 

Ultimately, however, as a subdelta extends farther into the bay and the gradient is diminished, it 

becomes less efficient and is unable to deliver and disperse sediments at a rate sufficient to offset 

subsidence over the larger subdelta footprint. Recent laboratory studies, summarized by Paola et 

1800 1850 1900 1950 2000

Year

0

200

400

600

800

Subaerial Areas (km

2)

West Bay

Cubit's Gap

Baptiste Collette

Garden Island Bay

Total
5

al. (2011), show that as relative sea level rise causes progradation to cease, the delta surface does 

not simply drown. Rather, the surface morphology appears able to adjust and thus accommodate 

more sediments, leading to the conclusion that experimental studies can help test the limits to 

which delta restoration can withstand subsidence without losing an unacceptable amount of 

subaerial land. It is noteworthy that during the deterioration phase as subaerial land was being 

lost in the Mississippi River subdeltas, the total volume of sediment in each subdelta continued 

to increase. Sediments were still accumulating but simply not at a rate sufficient to keep pace 

with relative sea level rise (sediment cores have revealed that subdeltas may be stacked upon 

each other, forming thick sequences in the geological record). Sediment supply thus becomes 

crucial as a suite of processes that, acting in concert, create a system that may be intrinsically 

capable of maintaining itself (Paola et al., 2011). 

However, the fact that the four subdelta deposits each underwent a deterioration phase while 

continuing to receive significant sediment discharge from the Mississippi River (75% of the 

original land area of the Cubits Gap subdelta had been lost by the late 1980s; Coleman, 1988), 

carries important implications for restoration, especially if it were to be undertaken in the lower 

delta. Implication #1: River diversions, which can be expected to have life cycles of decades to 

perhaps a century or more, like all coastal lands globally are not permanent features. Rather, 

they are part of a highly dynamic landscape. Implication #2: River diversions may be most 

effective if staggered in time and alternated between basins. Because there is a natural life cycle, 

subaerial land and ecological diversity could be maximized with multiple diversions, each of a 

different “age”. Implication #3: Predictions for subaerial growth using the subdeltas as a model 

would be unrealistic. Because the sediment load, specifically sand, in the Mississippi River has 

decreased on the order of 50% over the past 60 years or so, future diversions will have less 

sediment for land-building processes than before and, at the same time, will very likely face a 

higher rate of relative sea level rise. On the other hand, it is important to recognize that 

diversions built higher in the system (upstream of the modern birdsfoot delta) would almost 

certainly have greater longevity for reasons discussed later in this report. 

3.0 Variables that Impact Diversion Performance 

The performance of river diversions is controlled by numerous factors that can be broadly 

categorized as 1) basin geometry, 2) sediment characteristics, 3) biological factors, 4) water 

motion, and 5) design and operational strategies. Basin geometry includes size, degree of 

enclosure and the water depth, and is influenced through time by sea level rise and subsidence. 

Small, shallow basins develop subaerial land more quickly (other factors being equal), and 

enclosed or partially-enclosed basins retain sediments more effectively. Sea level rise and 

subsidence which, together, can increase water level by 2 cm/yr are also significant factors in 

modifying the size and thus geometry of receiving basins over periods as short as one to two 

decades. Recommendations for planning and executing small crevasse-splay diversions, based in 
6

part on research and past experience with basin geometry, are given by Turner and Streever 

(2002), but these would not necessarily be applicable to the siting of large land-building 

diversions in the upper reaches of the Mississippi River delta system. 

The quantity of new sediment that enters and is retained in a receiving basin must be sufficient to 

offset the effects of sea level rise and subsidence in order to build new land. Sediments that enter 

a receiving basin through a river diversion will be a mix of sand, silt and clay. The size 

distribution is of paramount importance in that sand is a key ingredient in building new land 

from diversions (Nittrouer et al., 2012). Bed load may be hard to capture and, even though sand 

often becomes a suspended-load component, sediment concentration profiles will affect the 

delivery of sediments given that shallow diversion cuts may not capture the higher concentration 

of sand that occurs in the lower part of the water column. Further, there may be an optimal 

coarse sediment time window, and inter-annual variability in sediment load is a common 

occurrence in the Mississippi River. Multiple “competing” diversions could certainly create 

complex relationships between flow and sediment. Finally, it is well established that suspended 

sediment loads in the lower Mississippi River have declined significantly during the latter half of 

the 20th century (Allison and Meselhe, 2010). 

Even if there is a generally-predictable relationship between the volume of water and mass of 

sediment that enters a receiving basin, the infilling process is controlled by the volume of 

sediment and the bulk density of the deposit. Biological factors are therefore notably important. 

Bulk density, defined here as dry mass per unit volume of the in situ deposit, is a measure that 

reflects the relative amount of organic versus inorganic sediment, and water content. Organic 

sediment, which may contribute more than 50% of the sediment volume is thus an important 

factor in diversion performance and is accounted for through “bulking factors” once a diversion 

deposit becomes subaerial. Moreover, wetland vegetation that is established at or about the time 

of land emergence helps bind the sediment through its root mass and trap particles from its 

above-ground biomass. 

Most large receiving basins, especially those that are open or partially enclosed, have tidal and 

wind-driven currents and can accommodate the generation of waves. Most basins are “leaky” in 

that the land is very low and can be overtopped during flood stage. Critical shear velocities for 

initiation of motion for fine-grained sediments are low (see next section) and these sediments 

could be resuspended and transported out of the basins. Major floods, while potential sources of 

high incoming sediment loads, can also cause scour within a receiving basin. Hurricanes can do 

the same, but there is continuing controversy as to whether significant amounts of new sediment 

enter the delta from offshore sources during hurricanes (Turner et al., 2006). With their higher 

settling speeds, sands would have shorter distances to reach the point of deposition (see next 

section) and are able to withstand water motion under a wider range of conditions than would be 

expected to occur throughout a hydrologic cycle. 
7

Finally, while not addressed in this document, diversion performance is dependent on diversion 

design and operation, including for example the degree of control over flow volume that may be 

addressed by engineered features or augmented by operational strategies. Pulsed introductions 

have been shown to affect sediment delivery because water diverted during rising and peak flows 

delivers more sediment per unit volume than during falling river stages (Day et al., 2009). Other 

strategies including allowing sediments to be stored in diversion access channels, pumping 

sediment from the bottom to ensure high sand loads, creating artificial marsh and employing 

pulsed introductions at key times during the hydrological cycle (Allison and Meselhe, 2010) are 

thought to be effective. In the following, we discuss only gravity-driven diversions and those that 

are not regulated by gates or other means.

4.0 Criteria for Deposition and Stability of Diversion Sediments 

4.1 Critical Shear Stress 

Consider a case of uniform depth in a receiving basin in which the velocity decreases with 

distance from the source. The distance to deposition will be controlled by at least two 

mechanisms. One is the threshold shear stress for scour and the second is the settling time of the 

sediments. The criterion for critical shear stress can be written as 

2

8 c c

f u ρ τ = (1) 

 

in which c τ is the critical shear stress, ρ the mass density of water, f the Weisbach-Darcy 

friction factor, and c u the critical velocity associated with the critical shear stress. A reasonable 

value of c τ for fine sediments (silt and clay) is 1N/m2

 (recognizing that very compact clays 

would be considerably less erodible) and for a Weisbach-Darcy coefficient of 0.08, the threshold 

velocity, c u , is approximately 0.32 m/s (=1.05 ft/s). For a water discharge Q from a small 

diversion opening and uniform angular spreading radial flow over an angle Δθ and uniform 

depth, h, the average velocity varies with distance, r, from the origin as 

Q

u

θrh = Δ . (2) 

Thus, the distance to which fine sediments could remain stable, c

r , for uniform angular 

spreading would be 

8 c

c c

Q Qf r

hu h

ρ

θ θ τ = = Δ Δ . (3) 
As an ex

the avera

distance 

1,

4.6 crπ =

Of course

greater p

4.2 Fall V

A second

suspensio

function 

decrease 

Figure 3.

It is seen

sediment

particle t

2 f

f

h

t

w =

Consider

ample, cons

age for the W

is 

,134

π (0.32)

 = 24

e, during flo

roportion of

Velocity 

d criterion is

on can fall to

of diameter 

the fall velo

. Fall velocit

n that for a se

t (Brown et a

o fall throug

. 

ring the same

ider a divers

West Bay Div

45 m. 

ood condition

f coarser sed

 that the dist

o the bottom

as shown in

ocity. 

ty vs. sedime

ediment size

al., 2009), w

gh one-half t

 

e geometry a

sion discharg

version. For 

ns the distan

iments woul

tance must b

m. This depen

n Figure 3 for

ent diameter

 of 0.01 mm

wf is approxi

the water dep

as before, th

8

ge of 40,000

a depth, h , 

nce would be

ld partially o

be great enou

nds on the fa

r the case of

r (Rouse, 193

m as measure

imately 0.01

pth, h (cons

he distance f r

0 cfs (1,134 m

of the receiv

e greater; how

offset this eff

ugh so that th

all velocity o

f quiescent w

37) 

ed in the Wes

1 cm/s. The t

sidered as re

f r associated 

m3/s) which 

ving waters 

wever, the d

ffect. 

he sediment

of the sedime

water. Turbu

st Bay studie

time, f t , re

epresentative

with the fall

is approxim

of 4.6 m, the

(4) 

discharge of 

t particles in 

ent which is 

ulence would

es for suspen

quired for a 

e), is 

(5) 

l time is 

mately 

e

a 

a 

d

nded 
9

f

f

Q

r

θw = Δ . (6) 

For the approximate West Bay Diversion conditions considered earlier, the distance, f r is 

1,130

0.0001 f r

π = = 1,897 m. (7) 

If the fine sediments aggregate as would be expected when riverine freshwater is discharged into 

a brackish environment, the fall velocity will increase, thus decreasing the fall distance; however, 

consideration of a radial velocity spreading model results in velocities that probably decrease too 

rapidly from the origin (the spreading would be more “jet-like” and thus spread more slowly) 

such that these two effects would tend to offset each other. In this example, using the two criteria 

and conditions evaluated, the required fall distance would be the limiting factor governing the 

deposition of the sediments. The fall velocity for sand (considered 0.2 mm) is 3 cm/s and the 

corresponding fall distance f r is 109 m. This finding is relevant to the proportion of retained 

sediment that should be considered in application of the simple geometric models presented here. 

Because the effects of turbulence will reduce the fall velocity, the fall distance approach 

described here will underestimate the fall distances. 

5.0 Simple Models For Scoping and Sensitivity Studies 

This guidance document presents analytical methods which can be applied to various diversionrelated tasks, including comparing different designs at one location, comparing the same design 

at different locations and conducting sensitivity tests. Several of the key input variables (e.g. 

subsidence, sediment delivered and retained, volume bulking due to vegetation and water 

content) are poorly known such that estimates must now suffice for diversions along the main 

stem of the Mississippi River. The philosophy associated with this method is that it represents a 

framework against which monitoring results can be compared and, on the basis of an adequate 

number of such comparisons, improvements made in the key parameters and/or methods. In 

applying the models, we recommend that better estimates of the key parameters be used as they 

become available. A central feature of the method is that no attempt has been made to calibrate 

with results from known diversions. For example, the calculations for the West Bay Diversion 

appear to differ significantly from the actual performance but, because the reason(s) for this are 

not known and this diversion has been in operation for less than 10 years, calibration efforts 

could target the wrong parameters/mechanisms. Rather, we consider it best at this stage to leave 

any difference as a cautionary notice to the User with the recognition that changes based on 

detailed monitoring are the only appropriate basis on which to develop modifications. In the 
10

following, the method is illustrated by application to hypothetical cases to illustrate principles, 

and to the West Bay Diversion and the planned White Ditch Diversion. 

Two simple geometric models of the evolution of diversion deposits have been developed. These 

models avoid many of the complexities of the evolutionary processes but allow the overall 

character of the diversion over time to be examined. The models include effects of the effective 

sediment discharge rate into the diversion, relative sea level rise, foreset slope and slope of the 

bottom in the receiving area. The advantages of these simple models are that analytical solutions 

can be obtained and they allow, for the first time, the long-term evolutionary characteristics to be 

examined. Further, they allow comparison of the performance characteristics of large vs small 

diversions, allow rational comparisons of the efficacies at different diversion sites and provide 

insight into the most relevant factors that govern performance. 

The two geometries that were examined include a truncated cone and a geometry of uniformwidth. The former is characteristic of the Wax Lake Diversion Delta and the second is similar to 

that of the planned White Ditch Diversion. It is found that in the presence of relative sea level 

rise, the subaerial deposit evolution occurs in three phases following the emergence of a 

subaerial platform: (1) a growth phase, (2) a phase in which the platform growth reaches a 

maximum and may display a period of stability, and (3) a phase in which the platform 

dimensions decrease and the platform finally becomes submerged. Following is a brief 

description of the two models, interpretation of model results and limited examples of the 

applications of these models. Other, more computationally intense models are available 

including those of Twilley et al. (2008) and Kim et al. (2009), building on earlier work by Parker 

et al. (1998), Kostic and Parker (2003) and Parker et al. (2008) and the Corps of Engineers 

models ERDC-SAND and ERDC-SAND2 models. The unique feature of the models presented 

here is their analytical character allowing features of diversions with different characteristics to 

be illustrated rapidly and the interrelationships between variables to be shown. 
11

5.1 Geometric Model 1: Truncated Cone, Uniform Depth

5.1.1 General 

The geometry of the truncated cone considered is presented in Figure 4. 

Figure 4. Definition sketch of a truncated cone in water of uniform depth. 

The volume of a truncated cone, V , is 

2 3

2

0 0 2 2 3

V rr

m m

θ αα

α

Δ ⎡ ⎤

= ++ ⎢ ⎥ ⎣ ⎦

 (8) 

where V Qt = and Qis the discharge rate of the retained sediments including “bulking” effects 

and t is time. We note from the above that the volume of the cone increases with the cube of the 

total depth, α . This is critical to the interpretation of the long-term evolution of diversion 

projects as the volume supplied is considered to be constant whereas the depth increase (due to 

subsidence and sea level rise) increases linearly such that the required volume to maintain the 

deposit subaerial increases with the cube of time as shown in Figure 5. 

0r

Rising Sea Level

m

1

Δθ

α

Subsiding Sea Floor

Deposit

Plan View

Profile
Figure 5.

The radiu

0 2

r

m

α = −

From this

radius wo

level rise

particular

evolution

5.1.2 Tim

In the pre

waters, s

platform 

It is fortu

to consid

graphical

. Interpretati

us, 0

r , of the

2V

m

α

α θ

+ −

Δ

s equation, i

ould increas

e, the radius 

r geometry a

n of the dive

me to Emerg

esence of a r

ediment disc

will never f

unate that thi

der only one 

l form with a

on of three s

e horizontal p

2

2 12m

α . 

it can be seen

e monotonic

will reach a 

and a relativ

rsion deposi

gence of a S

relative sea l

charge rate a

form. This is

is problem c

case for all c

additional de

stages of evo

portion of th

n that if ther

cally (as the 

maximum, t

e sea level ri

it. 

Subaerial Pl

level rise (RS

and the magn

 because the

an be solved

combination

etails in App

12

olution for tr

his cone is 

re were no re

square root)

then decreas

ise, this is an

latform for 

SLR), the co

nitude of the

e RSLR outp

d in a non-di

ns of parame

pendix B. 

runcated con

elative sea le

) with time. H

se and finally

n inescapabl

a Truncate

ombination o

e RSLR can 

paces the ver

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eters. The res

ne. 

evel rise (α =

However, w

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le consequen

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of depth of th

be such that

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form such th

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(9) 

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With this 

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h of the depo

hat it is neces

sented here 

the 

e sea 

g

osit. 

ssary 

in 
13

Defining a non-dimensional time, '

o

t

t

t

α

α

∂ = ∂ and a non-dimensional discharge, 

2

2

8 '

o

Qm Q

t

α θα

= ∂ Δ

∂

, 

it can be shown that the non-dimensional solution is 

( ) 2 3 1 3 ' ' 1 3( ') ( ') 0 − −+ + = tQ t t . (10) 

There is no solution to this equation for Q' < 2.25 meaning that for this range the deposit 

elevation does not reach the height at which the deposit could commence forming a subaerial 

platform. Figure 6 presents the relationship between the two non-dimensional variables, t ' and 

Q' . Note that the definition of the non-dimensional variables establishes the interrelationships 

among all variables. For example, in the non-dimensional discharge, Q' , the sediment discharge, 

Q , has the same effect on emergence time as the square of the initial depth, αo , or the inverse 

of the square of the foreset slope, m , etc. Examples will be presented later to illustrate 

application of the results. 

Figure 6. Non-dimensional time, t’, vs non-dimensional discharge, Q’, for truncated cone. 

0 5 10 15 20

Non-dimensional Sediment Discharge, Q'

0.0

0.2

0.4

0.6

0.8

1.0

Non-dimensional Time, t', to Platform Building

TPVSQP Aug. 25, 2012 5:58:23 PM

Minimum Q' = 2.25
14

5.2 Geometric Model 2: Uniform Width 

5.2.1 General 

The geometry for this model is shown in Figure 7. 

Figure 7. Uniform width model. Sloping sea floor.

The volume of the uniform width model with a horizontal bottom, is given by 

2

2 V Qt W xm

α

α

⎛ ⎞

== + ⎜ ⎟ ⎝ ⎠

, (11) 

and for the case of an emergent deposit, the value of x is expressed by 

2

1 2

W Qt

m x

W

α

α

⎡ ⎤ − ⎢ ⎥ = ⎢ ⎥

⎢ ⎥ ⎣ ⎦

. (12) 

After some algebra, the solution for the case of a finite bottom slope, mb , can be written as 

Subsiding Sea Floor

Rising Sea Level

1

1

x

mb

m

α h

x

W

Plan View

Profile View
15

( )

2 2

2 2 0

2 2( ) 2

bb b

b bb

mm m Qt

x x

mm mm mm W

α

α

⎛ ⎞⎛ ⎞ ⎜ ⎟⎜ ⎟ + + + + −=

⎝ ⎠⎝ ⎠ − −− . (13) 

5.2.2 Time to Emergence of a Subaerial Platform of Uniform Width and Depth 

For this case, the non-dimensional variables are 

'

o

t

t

W t

α

α

∂ = ∂ , the same as for the truncated cone; however, the definition of the non-dimensional 

discharge,Q' , differs and is '

o

Qm Q

t

α

α

= ∂

∂

. The governing equation, expressed in the nondimensional quantities is 

( ) 2 1 2 ' ' 1 ( ') 0 − −+ = tQ t (14) 

which can be solved directly for t ' as 

2 tQ Q Q ' ( ' 1) ( ') 2 ' = −+ − . (15) 

It can be shown that the minimum Q' for subaerial platform development is Q' = 2.0 compared 

to 2.25 for the truncated cone case considered previously. Details are presented in Appendix B. 

Figure 8 presents the solution for t ' as a function of Q' . 

Figure 8. Non-dimensional time, t’, vs non-dimensional discharge, Q’, for uniform width and 

uniform depth model. 

0 5 10 15 20

Non-dimensional Sediment Discharge, Q'

0.0

0.2

0.4

0.6

0.8

1.0

Non-dimensional Time, t', to Platform Building

TimeUnif Aug. 25, 2012 6:02:31 PM

Minimum Q' = 2.00
16

As for the case of a truncated cone, the form of the non-dimensional variables establishes the 

interrelationships among all variables. For example, in the non-dimensional discharge, the 

sediment discharge,Q , has the same effect on emergence time as the initial depth or the inverse 

of the foreset slope, etc. 

5.3 Examples Illustrating Application of the Two Models 

In the following, we present several examples to illustrate concepts and evolutionary features of 

diversion deposits. To provide perspective, estimates of the total annual delivery of sediments by 

the main stem of the Mississippi River ranges between approximately 35 x 106 m3 and 50 x 106

m3

 and the annual delivery of suspended sediments in the sand size range is estimated to be 

between 0.6 x 106 m3 and 10 x 106 m3 (Appendix A). Based on the relationships developed and 

recommended here for guidance, the ratio of sand to total sediment in suspension is 0.018 

(1.8%). 

5.3.1 Example 1. Case of Large Scale Diversion, Truncated Cone Geometry 

This example illustrates the evolutionary phases and time scales of a large diversion. Results are 

presented in Figure 9. A sediment diversion of this magnitude would represent approximately 

6% to 8% of the total inorganic sediment load of the Mississippi River or, if all of the diversion 

discharge were sand, up to 30% of the sand discharge. The characteristics of this example are 

shown in the figure caption. 

Figure 9. Example 1. Annual discharge of retained sediment = 3 x 106 m3/yr, initial depth of 

receiving waters = 2.0 m, elevation of horizontal portion of deposit above mean water level = 

0.25 m, rate of relative sea level Rise = 2.0 cm/yr, foreset slope = 0.002 and delta opening angle 

= 180o. 

0 200 400 600 800 1000

Years After Discharge Commences

0

20

40

60

80

Subaerial Area of Deposit (km2

)
17

This model application shows that the subaerial deposit first grows with time, followed by a 

maximum and then declines. As noted, the reason that the deposit evolves in this manner is 

related to the requirement for additional sediment vs time compared to the rate at which it is 

delivered as shown in Figure 5. For conditions considered here, the increased sediment 

requirement is ultimately greater than the supply. 

As shown in the preceding section, for the case of a truncated cone, the volume required to 

maintain a diversion platform relative to sea level varies with the cube of time (Eq. (8)); 

however, for the case of a diversion of uniform width, the required sediment varies with the 

square of time (Eq. (11)). 

5.3.2 Example 2. Large vs Small Diversions, Truncated Cone Geometry 

This second example examines the efficacies of larger vs. smaller diversions. Results are 

presented in Figure 10. In this example, the total volume of sediment retained in the deposits is 

the same except that in one case, the total sediment is distributed equally through two diversions 

and in the second, the total sediment is discharged through a single diversion. The two plots in 

Figure 10 thus represent the same total amount of sediment retained in the two diversions and the 

single diversion. It is noteworthy that the total subaerial area for the large diversion is 

substantially greater than the sum of the two volumes of the smaller diversions. Also, the time to 

emergence is shorter for the larger deposit than for the case of two smaller deposits. The reasons 

for this evolutionary behavior will become more evident later in this section. 

Figure 10. Example 2. Comparison of subaerial areas over time for one large diversion vs two 

diversions with the same total sediment retention. Initial depth of receiving waters = 0.75 m, 

elevation of horizontal portion of deposit above mean water level = 0.25 m, rate of relative sea 

level rise = 1.0 cm/yr, foreset slope = 0.002 and delta opening angle = 180o

. 

0 40 80 120

Years After Discharge Commences

0.0

0.1

0.2

0.3

Subareal Area of Deposit (km2)

Total For Two Diversions, 

10,000 m3

/yr Each

One Diversion, 20,000 m3/yr
18

5.3.3 Example 3. Uniform Width and Depth Model, General Evolutionary Characteristics 

This example portrays the evolutionary behavior for the case of a receiving area of uniform 

width and depth model with the characteristics shown in the caption of Figure 11. The same 

evolutionary phases are present for the uniform width model as have been shown for the 

truncated cone model and the same general interpretation of the causes apply. For this case, the 

receiving water depth αo of 2.0 m and a width W = 2,000 m results in a time to emergence of 

approximately 75 years. The extent, x , of the subaerial deposit peaks at approximately 290 years 

and becomes submerged at approximately 665 years after commencement of discharge. The 

sediment retention rate associated with this example represents from 0.12% to 0.17% of the total 

sediment discharge rate of the main stem of the Mississippi River or 6% to 10% of the total sand 

discharge. 

Figure 11. Example 3. Berm length, x , of deposit (see Figure 7) for diversion deposit of uniform 

width and into receiving waters of uniform depth. Annual volume of sediments retained = 60,000 

m3

/year, width of deposit = 2,000 m, initial depth = 1.5 m, elevation of deposit platform above 

water level = 0.25 m, relative sea level rise = 1 cm/yr. 

5.3.4 Example 4. Uniform Width Model, Effect of Bottom Slope 

This example illustrates the effect of bottom slope for the uniform width model. With an 

increasing depth with distance from the diversion location, the sediment discharged must fill an 

increasing depth and thus, the diversion is not as effective as for the case of a horizontal bottom. 

0 200 400 600 800

Years After Commencement of Diversion

0

100

200

300

400

500

x, Deposit Displacement (m)
19

Figure 12 shows that for the conditions indicated in the figure caption, an increase in bottom 

slope from 0.0 to 0.001, the long-term effectiveness of a diversion over a sloping bottom is 

reduced considerably. 

Figure 12. Example 4. Comparison of subaerial areas over time for two bottom slopes. Uniform 

width, annual retention of sediment = 200,000 m3

/yr, relative sea level rise rate = 1.0 cm/yr. 

Initial depth of receiving waters = 0.75 m, Elevation of horizontal portion of deposit above mean 

water level = 0.25 m, foreset slope = 0.002.

5.3.5 Example 5. Uniform Width and Depth, Effect of Relative Sea Level Rise 

This example illustrates the effect of relative sea level rise, a consideration when evaluating 

diversion sites at locations where the subsidence differs considerably. For conditions considered, 

Figure 13 shows that the greater relative sea level rise markedly reduces the diversion land 

building performance. 

0 200 400 600 800 1000

Years After Commencement of Diversion

0

5

10

15

Deposit Area (km2) 

Bottom Slope = 0.001

Bottom Slope = 0.0
20

Figure 13. Example 5. Comparison of subaerial areas over time for relative sea level rise rates, 

uniform width = 2,000 m, annual retention of sediment = 200,000 m3/yr. Initial depth of 

receiving waters = 2.0 m, elevation of horizontal portion of deposit above mean water level = 

0.25 m, foreset slope = 0.002, bottom slope = 0. 

6.0 Guidance for Selection of Diversion Parameters 

6.1 General 

This section provides recommendations for the quantification of parameters to be applied in the 

models described. The concept is to recommend methods of quantifying the parameters with the 

understanding that the values are approximate based on information and best judgment at this 

time. Thus, this guidance document represents a structure with which to compare monitoring 

results such that the methods and details will be improved as more information and experience 

become available. 

In the guidance recommendations presented in the following sections, it is assumed that the 

diversion hydraulics have been quantified in terms of their average annual flows. The parameters 

to be quantified for input into the models include: annual sediment input, proportion of sediment 

retained in the diversion deposit, sediment bulking factor, foreset slope and subsidence rate. 

Other required input parameters are considered User-specified and include: initial depth of 

0 200 400 600 800 1000

Years After Commencement of Diversion

0

5

10

15

Deposit Area (km

2) 

RSLR = 1.0 cm/yr

RSLR = 2.0 cm/yr
21

discharge, receiving basin bottom slope, deposit angle or width, and future sea level rise. Prior to 

presenting our preliminary recommendations for input parameters, it is noted that all available 

diversions should be examined with special attention directed to those that are close and/or 

similar to the site of interest and those parameters should be weighed heavily in the parameter 

selection. Additionally, sensitivity tests are recommended to assess the significance of the choice 

of input parameters. 

6.1.1 Annual Inorganic Sediment Input 

The recommended annual inorganic sediment input is based largely on Allison and Mesehle 

(2010) during the 2008 flood at Empire, LA and requires that annual average water diversion 

discharge, QWater , be known with the consideration that there should be some similarity of 

normal and flood characteristics at various locations along the River. Thus, the recommendations 

below represent diversions that are free flowing unlike the Bonnet Carré spillway that is only 

opened during periods of high river flow (Nittrouer et al., 2012) 

It is recommended that the annual delivery of sand be according to the following 

36 Q Q sand = Water (16) 

and the annual delivery of fines 

2,000 Q Q Fines = Water (17) 

for a total 

2,036 Q Q Sed Total = Water . (18) 

In the above equations, the sediment discharges are in cubic meters per year and the average 

diversion discharge is in cubic meters per second. These recommendations are compared with 

more detailed estimates and measurements for the total Mississippi River and West Bay 

Diversion and White Ditch Diversion in Table 1. 

 
22

Table 1 

Comparison of sediment transport by river diversions on the basis of equations herein and other estimates 

River of Diversion Qwater (m3

/s) 

Average Annual 

QSed (m3

/year) 

Estimated by Other 

Means (Source) 

Method Suggested Here 

Mississippi River at 

Belle Chase 

17,000 56.4 x 106 (Total) 

11.6 x 106

 (Sand) 

44.8 x 106 (Fines) 

(Allison, Personal 

communication) 

34.6 x 106

 (Total) 

0.61 x 106 (Sand) 

34.0 x 106 (Fines) 

White Ditch Diversion 111 0.20 x 106 (Total) 

0.002 x 106

 (Sand) 

0.128 x 106

 (Silt) 

0.073 x 106

 (Clay) 

(Wamsley, 2011) 

0.23 x 106

 (Total) 

0.004 x 106

 (Sand) 

0.226 x 106

 (Fines) 

West Bay Diversion 1,130 2.63 x 106 (Total) 

0.28 x 106

 (Sand) 

2.35 x 106

 (Fines) 

(Allison, Personal 

communication) 

2.31 x 106

 (Total) 

0.04 x 106 (Sand) 

2.27 x 106

 (Fines) 

It is noted that the sand transport estimates above differ substantially for the Mississippi River at 

Belle Chase and West Bay Diversion. The reason is not clear as the equations for the column 

titled “Method Suggested Here” were based on measurements at Empire as reported by Allison 

and Mesehle (2010). 

6.1.2 Foreset Slope 

All depositional slopes on the lower Mississippi River are very gentle and here we rely on 

recommendations of Twilley et al. (2008) and Kim et al. (2009), building on earlier work by 

Parker et al. (1998), Kostic and Parker (2003) and Parker et al. (2008), in which their range of 

foreset slopes for the final deposit is between 0.002 and 0.005. The smaller slopes would be 

associated with the smaller grain sizes and the greater tidal current and wave action. Initial 

recommendations are presented in Figure 14 which also presents (in parentheses) recommended 

slopes for the early phases of the diversion in which only sand contributes to the deposit. In 

application of these figures, the values to be applied are to be interpolated from those shown at 

various locations along the main stem of the Mississippi River. 
23

Figure 14. Recommended values for foreset slopes. Values in parentheses apply to sand size 

sediment. 

6.1.3 Proportion of Diverted Material Retained 

The proportion of diverted material retained (<1.0) would depend primarily on the sediment size 

and the wave and tide energy in the receiving area. Figure 15 presents preliminary 

recommendations for this proportion. 

Figure 15. Preliminary recommendations for proportion of diverted material retained, FR. 
24

6.1.4 Subsidence

Figure 16 presents preliminary recommendations for subsidence rates in the literature (see 

Section 11.2.1). 

Figure 16. Preliminary recommendations for subsidence rates, Fs. 

6.1.5 Bulking Factors 

The bulking factor (>1) is defined as the ratio of the volume of the final matrix of water, organic 

and inorganic material to the in-place (voids included) inorganic sediment. This will increase the 

sediment volume once the deposit reaches the water surface allowing the organic constituents to 

contribute to the total volume. However, in applications here with the simple models, it is 

assumed that the bulking factor is constant. As for other factors, a low energy diversion 

environment will contribute to greater bulking factors. Figure 17 presents a preliminary estimate 

of bulking factors with the expectation that this figure will be improved with the availability of 

more data. 
25

Figure 17. Preliminary recommendations for bulking factors, FB. 

7.0 Examples Illustrating Application of the Recommended Methodology 

Two examples are presented that illustrate application of the recommended methodology to 

designs of particular interest. 

7.1 Planned White Ditch Diversion 

The parameters applied for the planned White Ditch Diversion are presented in Table 2. This 

diversion is best represented by the uniform width geometry model. Note that the quantity 

QSed Eff _ is the effective annual sediment retention ratee and incorporates effects of bulking and 

retention according to 

Q FFQ Sed Eff R B Sed _ = , where (19) 

QSed Eff _ would always be greater than QSed . (20) 

In this case, we first calculate whether or not, and if so, the time required for the deposit to 

achieve an emergent subaerial platform for various considerations of the sediment size classes. 

Table 3 presents the results. 
26

Table 2 

Summary of recommended input values for White Ditch and West Bay Diversions

Diversion QWater

(m3/s) 

QSed Total

(m3/year) 

QSand

(m3/year) 

Prop. 

Retained, 

FR

Fig. 13 

Bulking 

Factor, 

FB 

Fig. 15 

QSed Eff _

(m3/year) 

Subsidence 

Rate, FS

(m/yr) 

Fig. 14 

SLR, 

(m/yr)

White 

Ditch 

(Uniform 

Width) 

111 226,000 

(Eq. (18)) 

200,000 

(by Wamsley, 

2011) 

4,000 

(Eq. (16)) 

(2,030 by 

Wamsley, 

2011) 

0.85 12 2,600,000 0.006 0.003 

West Bay 

(Truncated 

Cone) 

1,134 2,310,000 

(Eq. (18)) 

2,630,000 

(Allison, 

Personal 

communication)

40,810 

(Eq. (16)) 

280,000 

(Allison, 

Personal 

communication)

0.5 4 4,620,000 0.015 0.003 
27

Table 3 

Calculations to time of emergence for various sediment delivery estimates 

 for the planned White Ditch Diversion 

The sand discharge based on Wamsley (2011) is 2,030 m3/year and 4,000 m3/year based on 

methods suggested here. The width of the deposit area is 8,500 m. The values of Q' , t ' , and t

are presented in Table 3 along with other variables considered. When only sand is considered the 

times to emergence range from 13 to 30.5 years. For the case of sand and silt and the steeper 

foreset slope, the time to emergence is 0.35 years; however, this is probably too optimistic. The 

more realistic estimate is probably in the range of 5 to 15 years. This case illustrates the 

sensitivity of the results to sand discharge and the associated slope. 

The uniform width and depth model was applied to determine the long-term evolutionary 

behavior of the White Ditch Diversion with the results shown in Figure 18 which considers the 

full sediment discharge and the other parameters listed in Table 3. It is seen that the method 

indicates that the deposit will become emergent in Year 2 after commencement of the diversion 

and that after 50 years, the subaerial deposit will be some 99.2 km2

 (24,500 acres) compared to 

the predictions in Wamsley (2011) on the order of 30,000 acres. The close agreement of these 

two estimates is considered somewhat fortuitous. However, examining Figure 18, the effect of 

the difference in times to emergence for the full sediment discharge (1 to 2 years) and that if only 

sand contributes to the emergence time (13 to 30 years) can be appreciated. This issue will be 

discussed further later. 

Q (m3

/y), (Basis) Foreset Slope, m 

Fig. 12 

Q' t ' t (years) 

4,000 (Sand, Method Here) 0.08 7.8 0.074 13.0 

2,030 (Sand, Wamsley, 2011) 0.08 4.0 0.173 30.5 

129,940 (Sand and Silt, Wamsley, 2011) 0.08 254.8 0.002 0.4 

203,030 (Sands, Silts and Clays, Wamsley, 2011) 0.004 19.9 0.027 2.0 

230,000 (Total Sediment, Method Here) 0.004 22.5 0.018 1.4 
28

Figure 18. Results from application of method to planned White Ditch Diversion. 

7.2 West Bay Diversion 

The characteristics of the West Bay Diversion by the method here are presented in Table 2. As 

for the previous case of White Ditch, it is of interest to calculate the time to subaerial platform 

emergence for various estimates of sediment size fractions and associated slopes. The two 

estimates of sand discharge are 280,000 m3

/yr and 40,000 m3/yr by Allison (personal 

communication) and method presented here, respectively. Results are presented in Table 4 and 

indicate a range of time to platform emergence from 0.9 years to 6.5 years. Based on monitoring 

results (Barras et al., 2009), these estimates may be too optimistic. Other combinations including 

the complete sediment discharge and associated milder slopes result in a range of 10.8 to 12.6 

years which seem more reasonable in view of the small subaerial deposits that formed after the 

2011 flood season. 

0 20 40 60 80 100

Years After Commencement of Diversion

0

50

100

150

Subaerial Area of Deposit (km

2) 
29

Table 4 

Calculations of time of emergence for various sediment delivery estimates 

 for the West Bay Diversion 

Q (m3

/y), (and Basis) 

Foreset Slope, m 

Fig. 12 Q' t ' t (years) 

40,810 (Sand, Method Here) 0.02 15.3 0.023 6.5 

280,000 (Sand, Allison) 0.02 105.3 0.0032 0.9 

2.31 x 106 (All Sediment, Method Here) 0.002 8.7 0.044 12.6 

2.63 x 106 (All Sediment, Allison) 0.002 9.9 0.038 10.8 

The calculated long-term results for the case of a truncated cone and a deposit angle of 180o

including the effects of bulking and other factors presented in Table 4 are presented in Figure 19. 

This method predicts that in Year 50, the subaerial deposit will be 21 km2 (5,200 acres) 

compared to the first estimate of 9,800 acres http://lacoast.gov/reports/gpfs/MR-03.pdf . Based 

on earlier monitoring results (Barras et al., 2009), these estimates initially appeared to be too 

optimistic; however, the record flood of 2011 which led to the growth of new subaerial land in 

the form of small islands (Kolker et al., 2012) suggests that this may not be the case. 
Figure 19

8.0 The R

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30

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31

stakeholder collaboration. Clearly, there must be a commitment to adjust direction as new 

information becomes available, and a willingness to identify new information needs, and to 

develop and use new monitoring tools. Site-scale learning will be of immense value in evaluating 

and implementing future projects. Adaptive management will put what is learned to work. 

The basic elements of a monitoring plan must include: 1) Commitment to a long-term approach. 

Project success cannot be adequately gauged and adaptive management cannot be implemented 

unless monitoring is conducted for the duration of the project, scaled at the appropriate level for 

the size and importance of the project. 2) Acquisition of accurate bathymetric and subaerial 

surveys. Field equipment and remote sensing techniques are widely available and not costprohibitive for conducting rapid surveys with a high degree of accuracy. These tools should be 

routinely used. 3) Implementation of a monitoring frequency that ensures capturing the relevant 

details of change. At a minimum, observational data should be acquired annually with additional 

monitoring to take place when high impact events such as major floods or hurricanes occur.

Although it has been hypothesized that failure of the West Bay Diversion project was in part a 

result of Hurricane Katrina, the absence of monitoring before and after this event will prevent 

that important question from ever being answered. 4) Acquisition of bottom samples and cores. 

Data on sediment size and accumulation history are critical in evaluating the success of any 

diversion project and for predicting patterns and rates of future land growth. Radiometric tracers 

(

7

Be, 137Cs, 210Pb) can provide depositional history on time scales of weeks to centuries. 5)

Acquisition of water and sediment discharge characteristics through the diversion into the 

receiving basin. Accurate data on material passing through a diversion is essential for 

interpreting performance. 6) Acquisition of data on flow field and sediment concentrations within 

the receiving basin. Likewise, accurate data on material that moves through the receiving basin is 

essential for understanding sediment retention and for interpreting success. 7) Commitment to a 

data management plan. Data must be made available and disseminated to stakeholders in a 

timely fashion. It is suggested that monitoring could be improved based on the predictive 

methods of this guidance document. 

9.0 Improved Method for Applying Models 

The role of the sand component in building the initial platform for a diversion deposit has been 

noted throughout this document. However, the methods presented consider only one sediment 

type discharge throughout the deposit evolution. It is recommended that (1) only the sand 

fraction be considered as effective in the construction of the deposit until it becomes emergent, 

after which vegetation can commence to develop and act to trap the finer sediments, and (2) once 

an emergent platform has developed, the total sediment retained (including “bulking” by 

vegetation) be considered in the long-term evolution of the long-term diversion deposit. This 

requires a simple adjustment to the two models presented earlier such that the effective sediment 

discharge is increased by a factor following the emergence of the deposit. 
32

First the model is applied with only sand discharge and the steeper foreset slope (Figure 14) 

associated with sand to determine the time to emergence. It is noted that the time to emergence 

depends on the non-dimensional discharge (Q' ) definitions, and that the smaller sand discharges 

and larger foreset slopes in the emerging phase and larger discharges and milder slopes in the 

following phases tend to compensate. For the truncated cone, 2 Q Qm '∝ and for the uniform 

width case, Q Qm ' ∝ . An additional factor that can reduce or increase the effects on the 

emerging and later phases is the magnitude of the Q' values in the Q' vs t ' plots (Figures 5 and 

7). If the Q’ values are large and on the nearly horizontal portions of the relationships, the 

differences will be small. 

As noted, first the sand discharge and steeper foreset slope will be applied to determine the time 

to emergence. Secondly, the evolution will be calculated with the total sediment and milder 

foreset slope. The times from the latter calculation will then be offset such that the time to 

emergence is the same as determined in the first calculation. 

10.0 Lessons from Previous Diversions 

Undoubtedly the sedimentary processes associated with diversions are complex and 

interconnected, and there are no systematic studies dealing with them. The drivers are the 

climatic and oceanic conditions, inputs of water and sediments, geometric aspect of the diversion 

and physicochemical and sedimentary processes. Models dealing with diversions do not take into 

account these in detail, and model validations will be a requisite in such studies. A few 

diversions have received detailed scrutiny (West Bay) but some others (eg, Bayou Lamoque) are 

poorly documented. Table 5 is based on observations reported from a number of diversions, and 

general trends therein clearly demonstrate the importance of underlying processes; for example, 

the land gained over a period of years can possibly be eroded significantly by a single hurricane. 

Table 5 

Background on other diversions 

Diversion Purpose Capacity Comments 

Bonnet Carré 

Spillway 

(since early 

1930s) 

Flood protection 

(as needed; when 

river flow > 

35,375 m3/s). 

Operated 10 

times since 

construction. 

7,075 m3/s, 

gated 

Not optimized for water/sediment 

ratio; most sediment falls out within 1-

2 km; velocities (< 0.6 m/s) lead to 

beneficial sediment accretion for land 

building; temperature difference 

between river and marshes reduces 

vertical mixing; opened 42 days during 

the 2011 flood and resulted in the 
33

deposition of 3 million m3 of sand 

(Nittrouer et al., 2012). 

Caernarvon 

(small, lower 

Mississippi; 

since 1991) 

Limit salt water 

intrusions; 

minimum 

sediment capture 

100 m3/s, 

gated 

(maximum 

285 m3

/s) 

Expects to reduce marsh loss by 

82,700 acres in 50 years. Prior to the 

diversion, the land loss in the area was 

1000 acres annually, but in 1992-4, the 

land growth rate was 406 acres. A 

significant increase of wetlands and 

wild life was observed. Caernarvon 

area was the epicenter of land loss 

during Katrina due to winds and waves 

and velocities. 

Davis Pond 

(operated since 

2002) 

Limit salt water 

intrusions with 

minimum 

sediment capture 

225 m3/s; 

Rated – 300 

m3/s, gated 

 Expected to preserve ~ 33,000 acres in 

50 years; so far has been losing land; 

water quality issues because of 

insufficient circulation; concerns over 

freshening bay area (detrimental to 

oysters). 

Bayou Lamoque 

Diversion (two 

diversions; built 

(115 m3/s, 1955); 

225 m3/s (1978) 

Freshwater 

diversion; 

intermittent 

operation, not 

monitored 

Gated, but 

planned for 

365 m3/s 

without 

gates 

Relatively small land loss in the area 

after the diversion, but little 

operational data exists. New free 

flowing structures are expected to 

provide 620 acres of wetlands in the 

next 20 years. This modification 

authorized in 2006 but not yet 

constructed. 

West Bay (since 

2004) 

Land and 

wetland building 

570 m3/s, 

with 

potential to 

increase 

1,415 m3

/s 

Predicted to build 9,831 acres of 

vegetated wetlands in 20 years; West 

Bay was not successful for land 

building until the record flood of 2011, 

but land loss was greatly reduced 

during 2001-2009 (Barras et al., 2009). 

Only areas with pumped sediments 

gained new land initially. May have 

caused downstream shoaling leading to 

a 2010 decision to close the diversion; 
34

however, it remains open in 2012. 

Myrtle Grove 

(authorized in 

2001), now deauthorized, 

engineering and 

design studies 

continue. 

Land building, 

coupled with 

pipeline 

conveyance; 

includes reversed 

flow inflow 

channels for 

sediment capture 

425 m3/s, 

gated 

Goal is to maintain 33,880 acres of 

marsh areas over 50 year period; 

modeling shows pulsed operation is 

beneficial; options of placing dredged 

sediments only (so far ~500 acres has 

been created) versus the efficacy of a 

diversion are evaluated; concerns of 

excessive freshening that harm 

fisheries. 

Cubits Gap 

(excavated in 

1862) 

To allow passage 

of shallow boats 

(initial width ~ 

120 meters, but 

after floods it 

expanded to 1 

km by early 

1900). 

10% of the 

total flow in 

the river 

Naturally evolved after an artificial 

crevasse. Initial building up of 

distributory channels, coarse sediments 

near the breach, shoaling in the bay by 

underwater deposition of finer 

sediments. Sediment deprivation in the 

1970s caused a large part of crevasse 

system to be inundated by seawater. 

Illustrates the cycle of delta lobe 

building and abandonment, with time 

scale ~100 years (Wells and Coleman, 

1987). 

Many questions remain on the effectiveness of diversions in land building: For example, how 

large should the diversion be; where should be it placed; how much water should be diverted; 

should it be gated or natural; what optimal geometry and sill height should be used; how do the 

characteristics of the receiving area respond to sedimentation; when should sediment trapping 

devices be introduced; should water be diverted in a continuous or pulsating manner; how much 

land building is expected near/intermediate and long-term; what is the useful life of the 

diversion; and should each diversion be operated independently or as a group? Related issues 

also arise with regard to bio-geo-physical interactions such as the adverse effects of high nutrient 

loads carried by the river in creating dead zones in diversion areas and its effect on fisheries. The 

impacts on navigation are also important, and simple fluid mechanical arguments suggest that the 

shoaling is unavoidable for straight reaches. The influence of curvature and secondary 
35

circulations need to be understood so the basin scale implications of operating diversions can be 

established. A vexing question is the economics of diversions: can beneficial use of sediments be 

an alternative, not a supplement or operating in tandem, to diversions? Monitoring of the recent 

land building at West Bay during the floods of 2011 will provide valuable information relating to 

the role of episodic events. 

11.0 Summary and Recommendations 

11.1 Summary of Methodology and Parameter Selection 

River diversions are considered as one of the most effective approaches to restoration and 

maintenance of wetland areas, in part because they mimic natural processes. Diversions 

considered here are those in the free surface, freely flowing class, i.e. no gates, siphons or 

pumped delivery. 

This guidance document has presented methodology and recommended parameters for 

preliminary evaluation of the efficacy of diversions of various sizes and locations. Two simple 

models for deposit geometry are presented: a radially symmetric truncated cone which is similar 

to the Wax Lake Diversion, and a deposit of uniform width which is more like the planned White 

Ditch Diversion. 

The advantage of guidance such as presented here is that a fixed methodology is defined against 

which past and future experience and monitoring results can be compared, thereby providing a 

basis for objective refinement of the overall method as well as conducting sensitivity studies. It is 

envisioned that results presented in this document can be applied to provide preliminary 

screening and comparison of conceptual designs at different sites or different design 

characteristics at one site. Recommendations are presented for annual sand and total sediment 

discharge as simple proportions of the annual average water discharged through the diversion. 

Recommended parameters recommended as functions along the main stem of the Mississippi 

River include: subsidence rates, foreset slopes, bulking factors, and proportion of material 

retained. 

For each of the two geometric models, methods are presented for calculating time to emergence 

and the long-term evolutionary behavior. For the time to emergence, it is recommended that only 

the coarser fraction of sediment be considered along with an appropriate foreset slope. The 

results suggest that formation of the initial deposit primarily from the sand size fraction may be a 

critical phase in the success of the diversion. A significant result for the long-term evolution is 

that, for the geometric models examined in the presence of relative sea level rise, three 

evolutionary phases are found: an emergence and growth phase followed by a maximum land 
36

area and finally a decrease and submergence of the subaerial platform. Within the limitations of 

the models examined, this evolutionary behavior is an inescapable result of the effect of relative 

sea level rise and is due to the fact that the required sediment delivery rate to maintain the 

deposit above water increases with time while the rate of sediment delivery by the river is 

considered to remain constant. This eventual submergence is consistent with the studies of Wells 

and Coleman (1987) in their examination of the evolution of four historic subdeltas in the lower 

Mississippi River system (Figure 2) and is also consistent with the formation of floating marshes. 

Although sediment retention devices, such as artificial islands or sills could improve the 

performance of diversions, they have not been addressed here. Finally, the 2011 floods on the 

Mississippi River and the associated land building at West Bay Diversion provide an opportunity 

which, if well monitored, can advance our understanding of these processes significantly. 

11.2 General Recommendations for Parameter Selection 

11.2.1 Subsidence Rates and Sediment Retention

Subsidence is particularly problematic because the ability of river diversions to become subaerial 

features is tied explicitly to the balance between sediment, primarily sand, that is delivered and 

remains in the receiving basin, and relative sea level rise which is likely, but not necessarily, 

dominated by subsidence. Moreover, there is considerable controversy over actual subsidence 

rates, the relative contributions from deep versus shallow processes, impact from human 

activities, the effects of measurement techniques on determination of rates, the potential for 

significant impacts from growth faults, and the changes in subsidence rates over time (Dokka et 

al., 2006; Gonzalez and Tornqvist, 2006; Meckel, 2008; Tornqvist et al., 2008; Morton and 

Bernier, 2010; Kolker et al., 2011)). In short, relative to its importance, we know less about 

subsidence than any other process that will affect the success of river diversions. However, it is 

crucial that lack of consensus on the above issues not lead to inaction. We thus offer the 

following general guidance: 1) Select sites that, based on all available evidence, are in areas of 

low subsidence. Diversions above Myrtle Grove would be favorable and below Venice would be 

highly unfavorable. 2) Select sites that have relatively thin Holocene sequences. There is general 

agreement that compaction and other shallow processes will be lower in sediment sequences that 

are thin and contain less organic material. 3) Select sites that are likely to have very high 

trapping efficiency. Given the uncertainty in subsidence, retention of sediments should become a 

first-order consideration and be maximized. This also argues strongly for diversions that are in 

the upper part of the distributary system. Rapidly subsiding open bays on the lowermost delta are 

unlikely to offer the physical characteristics necessary for success. 

11.2.2 Delta Opening Angle and Diversion Depths and Slopes 

Flow from the main stem of the river through a diversion opening into a receiving basin will 

expand and decelerate, providing the potential for subaqueous deposition of sediments that over 
37

time could aggrade to create subaerial land. As the pipeline for supply, the diversion cut must be 

located and oriented to maximize the opportunity for self organization of water and sediments 

into a channel network once reaching the receiving basin while, at the same time, reaching deep 

enough vertically to capture and deliver sand into the basin. The basin itself must be sufficiently 

shallow to create the best opportunity for land growth. We offer the following guidance: 1) 

Select sites that do not exceed 2 m in depth. The shallower the depth, the sooner new land will 

appear (other factors being equal) and the faster new land will accumulate. The highly 

successful Wax Lake Delta in Atchafalaya Bay has been building in a receiving basin that is only 

2 m deep and, as a result, has added 100 km2 of new land in only 30 years. 2) Use numerical 

simulation to determine ideal opening angles. The effects of meander bends and thus the angle of 

a diversion opening could be important in sediment delivery through the diversion. 3) Select sites 

that have very low bottom gradients. Atchafalaya Bay constitutes an ideal receiving basin 

because it is relatively flat such that progradation requires less sediment volume per unit of new 

land than a sloping bottom. 

12.0 References 

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Mississippi River (Louisiana) for Coastal Restoration. Journal of Hydrology 387:346 -360. 

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Analysis of the West Bay Sediment Diversion Receiving Area, Louisiana. Report for U.S. Army 

Engineer Distriction, New Orleans (MVN), 39 pp. 

Brown, G., C. Cullegan, R. Heath, L. Hubbard, C. Little, P. Luong, K. Martin, P. McKinney, D. 

Perky, F. Pinkard, T. Pratt, J. Sharp, and M. Tubman. 2009. ERDC Workplan Report-Draft: 

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Coleman, J.M. 1988. Dynamic changes and processes in the Mississippi River delta. Geological 

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models of deltaic sedimentation. Louisiana State Univ., Coastal Studies Inst. Ser. Bulletin 3:23-

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Coleman, J.M., H.R. Roberts, and G.W. Stone. 1998. Mississippi River Delta: an Overview. 

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Davis, D.W. 2000. Historical Perspective on Crevasses, Levees, and the Mississippi River. In: 

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and B. Wissel. 2009. The impacts of pulsed reintroduction of river water on a Mississippi Delta 

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displacement of southeast Louisiana with respect to stable North America. Geophysical Research 

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Edmonds, D.A. and R.L. Slingerland. 2007. Mechanics of river mouth bar formation: 

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Meckel, T.A. 2008. An attempt to reconcile subsidence rates determined from various techniques 

in southern Louisiana. Quaternary Science Reviews 27:1517-1522. 

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A‐1

Appendix A 

Useful Conversion Factors (Some are Approximate) and Estimates 

A.1 Useful Conversion Factors

1 Megaton (MT) of Sediment = 580,000 m3 prior to bulking 

1 mg/Liter = 10-12 MT/m3 

1 cfs = 0.0283 m3/s

103 Liters = 1 m3

1 Pascal = 1 Newton/m2

 = 0.1 dyne/cm2 

1 Acre = 0.405 Hectares 

1 Hectare = 2.47 Acres 

1 km2

 = 247 Acres 

A.2 Useful Estimates 

Average water discharge of the Mississippi River = 17,000 m3/s = 600,700 cfs 

Average annual sediment discharge of the Mississippi River = 35 x 106

 m3/y to 50 x 106 m3/y 

Average annual sand discharge of the Mississippi River = 0.6 x 106

 m3/y to 12 x 106 m3/y
B‐1

Appendix B 

Time to ‘Platform Building” 

B.0 General 

This appendix addresses the time to “platform building” of a deposit for a truncated cone and a deposit of 

uniform width. 

B.1 Truncated Cone 

The elevation, h of a cone prior to platform building to the deposit height is related to the volume as (see 

Figure 4 for definition of variables) 

2 3

2 6 6

hR h V Qt θ m θ == = Δ Δ . (B.1) 

The total heightα required to commence platform building is o t

t

α

α α

∂

= +

∂ . Equating h and α yields 

2 3 2

32 2 3 33 0 oo o

m Q tt t

t tt

α αα

αα α

θ

⎛ ⎞ ∂ ∂∂ ⎛ ⎞⎛ ⎞ + −+ + = ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠ ∂Δ ∂ ∂ ⎝ ⎠⎝ ⎠ . (B.2) 

Defining a non-dimensional time, '

o

t

t

t

α

α

∂ = ∂ and a non-dimensional discharge, 

2

2

8 '

o

Qm Q

t

α θα

= ∂ Δ

∂

, the 

above equation reduces to 

( ) 2 3 1 3 ' ' 1 3( ') ( ') 0 − −+ + = tQ t t , (B.3) 

which must be solved by iteration. The above form is convenient as there is only one independent 

variable, Q' . It can be shown that there is no solution for Q' < 2.25. For Q' < 2.25, the deposit height 

does not reach the height at which the deposit would commence forming a platform. Figure B-1 presents 

the relationship between the two non-dimensional variables, t ' and Q' . 
B‐2

Figure B-1. Non-dimensional Time, t’, vs Non-dimensional Discharge, Q’ for Truncated Cone. 

B.2 Uniform Width and Depth Case 

For this case, the equation for the deposit height prior to platform building is (see Figure 7 for definitions 

of variables) 

2

2 2

Whx Wh V Qt

m == = . (B.4) 

Equating h and α yields 

2

2 2 2 0 o o

mQ t t

tW t

α α

α α

⎛ ⎞ ⎛⎞ ∂ ∂

+ −+ = ⎜ ⎟ ⎜⎟ ⎝ ⎠ ⎝⎠ ∂ ∂ . (B.5) 

Again defining non-dimensional variables as 

'

o

t

t

t

α

α

∂ = ∂

 and '

o

Qm Q

t

α

α

= ∂

∂

 and the above equation, expressed in the non-dimensional quantities is 

( ) 2 1 2 ' ' 1 ( ') 0 − −+ = tQ t , (B.6) 

which can be solved directly for t ' as 

0 5 10 15 20

Non-dimensional Sediment Discharge, Q'

0.0

0.2

0.4

0.6

0.8

1.0

Non-dimensional Time, t', to Platform Building

TPVSQP Aug. 25, 2012 5:58:23 PM

Minimum Q' = 2.25
B‐3

2 tQ Q Q ' ( ' 1) ( ') 2 ' = −+ − . (B.7) 

It can be shown that the minimum Q' = 2.0. Figure B-2 presents the solution for t ' as a function of Q' . 

Figure B-2. Non-dimensional Time, t’, vs Non-dimensional Discharge, Q’ for Uniform Width Model. 

0 5 10 15 20

Non-dimensional Sediment Discharge, Q'

0.0

0.2

0.4

0.6

0.8

1.0

Non-dimensional Time, t', to Platform Building

TimeUnif Aug. 25, 2012 6:02:31 PM

Minimum Q' = 2.00