Compressing a century into 7 days
A physical model of part of the Mississippi Delta, now operating in Louisiana USA, has given legislators and engineers a better understanding of the complex interactions that are involved in the river dynamics. Acker explains how its unusually small scale allows a century to be compressed into 7 days but that it also demands a high degree of accuracy in its construction and choice of simulated sediment.
The capricious Mississippi River has been outmanoeuvring man for hundreds of years, responding to attempts to channel it, dredge it, contain it and generally tame it by forming new courses. It floods with increasing intensity and spews enormous areas of precious land into the Gulf of Mexico. New Orleans once had levées 1 m high to protect it; now they are 10 m high and offer no absolute guarantee against inundation. Because of the way the river has evolved during the last 200 years, and because of subsidence, the modern part of the city is now about 5 m below the Mississippi, and the river’s elevation is such that streams tend to flow away from the Mississippi rather than into it. Four major river drainage systems flow out of the northeastern hills of the state into the Delta and finally empty into the river.
The devastating flood of 1927 has already gone into the folklore; three separate flood waves occurred on the lower Mississippi that year – in January, February and April – each increasing in level compared with the one before. The river breached levées in seven states (Arkansas, Illinois, Kentucky, Louisiana, Mississippi, Missouri and Tennessee) and flooding an area of approximately 60,000 km2 (23,000 miles2), killing 500 people, forcing 700,000 from their homes, and destroying nearly US$400 million worth of property.
Part of the problem is that as it nears the end of its 6000 km (3700 mile) journey and moves into the Mississippi Delta, the river becomes wide and shallow, which makes it difficult to contain during high flows and difficult to navigate during low flows. Constant and costly dredging keeps the navigation channels open for most of the year, but heavy rains, tropical storms, and hurricanes, which are common to the area, can and frequently do, disrupt routine maintenance. After severe weather many cities along its route become flooded, causing loss of life and economic devastation. The river, along with the Missouri and Ohio, which are its main tributaries upstream, drains 44 per cent of the land area of continental USA, so that the waterway is a critical component of the economic health of the country and especially to the 15 States through which it runs.
The land area lost each year is 80 km2 and the volume of total sediment about 150 to 200 million tons. The immediate effect of the sediment loss is the impoverishment of the Delta itself; but also because it is deposited in the Gulf, this combined with the levée system along the banks has extended the river length further downstream. This has caused the riverbed upstream to rise to overcome the additional river length; the effect is to increase its height over the flood plain.
In one of the measures being taken to assess what is seen as an increasingly difficult problem, the Office of Coastal Restoration and Management of the Louisiana Department of Natural Resources commissioned a small-scale physical model of the lower part of the river and the Delta, beginning with a detailed aerial survey comprising two hundred ground profiles sections carried out by a Louisiana surveying company C & C Technologies. In addition, cross-sections of the riverbed at 600 m intervals were taken (totalling 185 spaced at 5 cm intervals on the model) and were transferred to the model. The work of making, verifying and calibrating the model was carried out at the Sogreah Laboratories in Grenoble, France, under the direction of Sultan Alam, of Coastal Restoration Consultants, Louisiana.
The model is physically quite small – possibly one of the smallest ever built to simulate a riverine area. Its size allows a very fast time simulation, 30 minutes corresponding to one year. In addition, the quantities of simulated sand and the amount of water are less than with a bigger model, making it easier to operate. Finally, it was quicker to build with consequent cost savings, while giving a faster response to the client’s needs. Made of polystyrene surfaced by a thin layer of impermeable glass fibre, it measures 8.46 m × 7.41 m, giving an area of 62.69 m2, corresponding to an actual prototype surface area of about 9000 km2 (3500 miles2), including the lower 122 km (76 miles) of the river.
The model was built in ten weeks. Although exact figures are confidential, it is generally accepted that the cost of the physical model is much less than that of an equivalent mathematical model and quicker to build. The model’s dynamics are based on Froude similarity laws for the hydraulics and Shields’ law for the transport of sediment.
The sand grains vary from 0.06 mm to 0.3 mm and are represented by a granular synthetic material with a specific gravity of 1.05, compared with the Mississippi’s sand of 2.65. Sand comprises 25 per cent of the total sediment load in the river in the area under observation, and the model accurately represents the sand’s transport and deposition characteristics. The actual sand load transported over one year is about 20 million tonnes, and the simulated load is 0.23 kg. Had the model been larger the weight of simulated sand would have been larger too, and it would have taken longer to run for a given time frame.
The density ratios of the model and prototype are related to the ratios of the model and prototype water velocities. Various low density materials were tested until an exact correlation was obtained between the behaviour of the prototype sand and the low-density grains were obtained.
The remainder of the sediment load is silt and clay, which by definition is always in suspension, and its deposition patterns in the marshes will be determined first with dye injection and time lapse photographs and then will be accounted for using a well-known numerical model called HEC6. It is the sand’s behaviour that is of interest to the clients because once that is understood and anticipated, then it will be possible to understand, or at the very least, to predict the fine sediment’s response to interventions and varying river conditions.
The water, of course, is not simulated, so that a careful balance has to be made between the model flow rate, determined by its vertical and horizontal ratios, and the model head. The distortion (the different scales used for the vertical and horizontal dimensions) is necessary given the model’s size, but its specific purpose is to reproduce the general trend of sediment transport rather than other parameters such as secondary currents.
The selection of the model sediment material was based on the criteria of equivalent prototype and model sediment transport characteristics – that is, various stages of transport such as incipient sediment particle movement, formation of dunes, generalised bed movement and transport in suspension. Prior flume tests allowed verification of the model sediment material behaviour in reproducing the transport characteristics.
The model’s water is supplied through a weir and flow divider, which can be easily adjusted to provide the required water discharge; this point corresponds to the town of West Pointe à la Hache. The sand starts to be transported at flow rates of 11,300 m3/s and above, so model tests began with simulating this value and progressed in steps to 35,400 m3/s, which is the peak flow for the river in this reach between October and May.
Once the model was constructed it had to be mounted on a rigid base, and rigorously checked so that the model heads corresponded to actual heads throughout the 9000 km2 under study. This is a delicate and exacting task; with the vertical ratio of 1:500, an actual head of say 20 m is represented by 4 cm on the model. Smaller heads need correspondingly finer adjustments. To ensure that the model’s water levels are measured precisely (+/– 0.25 mm) the gauging pins are adjusted to take into account the effect of surface tension at the pin itself. Each gauging pin corresponds to a gauging station on the river.
Altogether, 13 small diversion channels have been built on the model to assess how sediments may be dispersed into the surrounding marshlands. This arrangement has yielded some important insights into the efficacy of the process, and will help to select the best arrangement of remedial measures in the near future before undertaking the necessary design studies for the Louisiana Coastal Authority program.
The calibration consisted of running the model for a simulated 100 years (using an average 30-year hydrograph). The primary calibration parameter was matched with historical records, ensuring that the total amount of sediment removed from the model (overflow and dredging) matched the input sediment totals within a reasonable limit. The model also simulates relative sea level rise by adjusting it to correspond with a sea level rise of 30 cm (1 ft) every 25 years.
The model tests confirmed the frictional head loss and water surface gradient over the 129 river kilometres reproduced on the model for various river discharges between 11,000 m3/s and 35,000 m3/s. It also reproduced satisfactorily for the typical water year sediment deposition patterns over a certain reach of the main river arm and the annual volume dredged (9,000,000 tonnes) to maintain safe deep-water navigation channel in the lower reach of the river to its outfall in the Gulf of Mexico.
Since the model has been on display, particular interest groups, such as legislators, academics, and environmentalists, have been invited to observe it in operation. According to the Director of Coastal Engineering, Christopher Knotts, their reaction has been encouraging. Their understanding of the complexities of the Delta has been helped in a way that could not have been achieved with a numerical model. Some individuals were sceptical before seeing the model but changed their views when seeing how effectively it represented an area with which they were already familiar. Another useful characteristic of the physical versus a numerical version is, of course, the accelerated time frame possible, allowing 100 years of simulation to be compressed into one week.
While the Department of Natural Resources, a State body, is responsible for the restoration of Louisiana’s coastal area, the Corps of Engineers (a Federal body) is responsible for navigation and flood control on the Mississippi River. Therefore, the work of either one affects that of the other, and the model has been valuable in allowing both authorities to see where possible interventions may be advantageous to both parties; engineers from the Corps have visited the site on several occasions. A report written by Sultan Alam et al. was published in June 2004 (available after we had gone to press) with a range of recommendations based on model observations and suggestions for further studies.
Freelance Science Writer
Fabian Acker is a science writer, the Secretary of the Association of British Science Writers, and Senior Tutor at the National Council for the Training of Journalists. He is a Chartered Engineer, a member of the IEE and IMarestE and Consultant Editor for Hydropower & Dams.